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]]>A field bounded by three arms is called a triangle. According to Euclidean geometry, one and only one triangle can be drawn by three points which are not located in the same straight line. In other words, a polygon that has only three sides and three vertices is called a triangle. The vertex of a triangle refers to the point at which any two of its sides meet. Considering the number of sides, the triangle is the lowest polygon, that is, there is no polygon whose number of sides is less than three. The sum of the three angles of a triangle is two right angles or 180. Although it is a bit difficult to specify the number of types of triangles, the following is a list of the number of triangles that are usually found by considering the types of triangles by arm, types of triangles by angle and other features of triangles. In the figure, different types of triangles are seen. Equilateral triangles are common forms of all triangles. That is, other triangles are formed due to some features of the equilateral triangle. For example, if two sides of an isosceles triangle are equal to each other, then it becomes an isosceles triangle. A triangle whose only two sides are equal is called an isosceles triangle.

Again, in some cases it is said that at least two sides of a triangle are equal to each other, hence an isosceles triangle. In this case, all equilateral triangles can be called isosceles triangles. In other words, a triangle whose two angles are equal to each other is called an isosceles triangle. If the value of any one angle of an isosceles triangle is known, the measurement of the other two angles can be determined. In the figure, an isosceles triangle is seen. If the lengths of the three sides of a triangle are equal to each other, it is called an equilateral triangle. It is a balanced triangle because the lengths of its three arms are equal to each other. Again, the lengths of its three arms are equal, so the three angles are equal to each other. In the figure, an equilateral triangle is seen. In other words, a triangle whose angles are three equal to each other is called an equilateral triangle. The sum of the triangles of the triangle is 180. As a result, if the angles are equal to each other, each of its angles measures 70. So the measure of each angle of an equilateral triangle is 60.

Therefore, it can be said that each angle of the triangle measuring 60 ° is called an equilateral triangle. Moreover, an equilateral triangle is a balanced polygon with three sides. The reason for being a balanced polygon is that the arms of this polygon are equal to each other. If each of the three angles of a triangle is a right angle, it is called a right-angled triangle. The sides of a right-angled triangle can be equal to each other; Again, the arms can be unequal. However, if the lengths of the three arms are equal to each other, then it becomes an equilateral triangle. If two angles of a right-angled triangle are equal to each other, then it becomes an isosceles triangle. Three inscribed squares of a right-angled triangle can be drawn where one side of each square is part of one side of the triangle and the other two vertices of the square are located on the other two sides of the triangle. In the figure, a right-angled triangle is seen. If an angle of a triangle is obtuse, it is called obtuse triangle. An obtuse triangle can have only one obtuse angle. In the figure, an obtuse triangle is seen. Each of the two angles except the obtuse angle of this triangle is a fine angle. Again, the opposite arm of the obtuse angle of this triangle is the largest arm. Moreover, the sum of the three angles of a triangle is 180 ° and the sum of the other two right angles is less than one right angle except the obtuse angle of an obtuse triangle.

If one angle of a triangle is right angle then it is called right angle triangle. 1 right angle = 90. Complementary angles because the sum of these two angles is 90. The Pythagorean theorem is based on a right triangle. If the two sides of this triangle are equal to each other, it is called isosceles right triangle. Moreover, the two right adjacent sides of a right triangle are called perpendicular and ground. In the figure, a right triangle is seen. A right-angled triangle whose arms are not equal to each other is called an equilateral right-angled triangle. Again, the right angle of each of the three angles of the equilateral triangle is called the equilateral triangle. In the figure, an equilateral obtuse triangle is seen. Equilateral triangle is a right triangle on one side and an obtuse angle at an angle of the triangle is called equilateral triangle. Equilateral equilateral triangle as well as right-angled triangle and equilateral triangle. Again, the arms of this triangle are said to be unequal to each other, the three angles are also not equal to each other. In the figure, an equilateral obtuse triangle is seen.

A right-angled triangle whose three sides are unequal to each other is called an equilateral right-angled triangle. In other words, an angle of right angle of an equilateral triangle is called an equilateral right triangle. In the figure, an equilateral right triangle is seen. Equilateral right-angled triangle and right-angled triangle at the same time. Again, because the arms of this triangle are three unequal to each other, each of its right angles is called an isosceles right-angled triangle. Isosceles right-angled triangle on one side such as right-angled triangle; At the same time it is an isosceles triangle. Again, the two sides of this triangle are equal to each other; As a result, the opposite angles of its two equal arms are also equal to each other. If the measurement of one angle of this triangle is known, the measurement of the other two angles can be determined. In the figure, an isosceles triangle is seen. If two sides of an obtuse triangle are equal to each other, it is called isosceles obtuse triangle.

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]]>**derivative of arctan(y/x)**

We’re going to find the first partial derivatives of this function and evaluate them at 4, negative for let’s go ahead and go through it carefully before we do the **derivative of arctan(y/x)** for the call that the derivative of arctangent is 1 / 1 + x squared so if you just had DDX of arctangent say simply be well be 1/1 + x sqrt so we’re going to use this formula and this problem so first of time bail after sex so taxes owed LF du lac’s is the partial derivative with respect to X we do this all of the wise are constants.

Now we have an X in here so this is not a concert so we still have to use this formula so it’s going to be one 1/1 + one over one plus x squared but this is RX this whole thing so y over X squared times the derivative of the inside function so we have this piece with respect to X keeping in mind that why is a constant so what I’m thinking is we can think of Y over X eye x 1 / X which is why y x x times x to the negative 1 one and why is a constant.

when you differentiate this is putting negative in you say tract you subtract one right you just differentiate the X and Y & Y without cuz it’s a constant and I think I’m going to write it like this so this is going to be negative y over x squared over / 1 + y squared over x squared by squaring each piece then bring this down in writing it like outside that s basically wrote that here this is up top and then.

We have that on the bottom so now what we can all we can do is we can * x squared over x squared to clean things up to do the t do that that please cancel so we get Negative why is really beautiful export * 1 is simply t time e is it that cancels so you get white square to Waterford answer so that my friends would be dull F 2X Dell Optiplex be driven of a bath with respect to X 2 slope in the X Direction x-direction. why so tell f F. Why all this would be 1 / same thing 1 + y over X quantity squared times the derivative of the inside function so now we’re taking the derivative with respect to y Sol so I can’t you can think of it like this

The derivative of y is one the one over X hangs out so you just get x 1 / X that’s all you would get there I believe yep yep that’s it because like the ore like before the derivative of wise one and this just hangs out I’m going to write it like this one over x / 1 + y squared over x squared and I’m leaning towards doing something similar so let’s go ahead and put (here in) here hear the same thing as x x squared over x squared just to make it look better.

I mean to do that by we can do that by the way we’re basically multiplying by 1/4 I do this you lose Annex here so you get EX and then here export * 1 is x squared x squared times this to get a y squared really really cool really pretty looking derivatives difference at this point this is your ex this is your way so let’s do the LF The Lacs at 4 four negative four for a negative for that would be this your wires negative form is already negative here so it’ll be a positive for on the bottom you get for his purpose for Aquarius so you get 16 + 16 16 + 16 + 4/32 before goes into for one time.

32 so it’ll be 1/8 so this would be could be the slope and the extra action at that point now it’s fine in the other one at the same point so dull F the Y at four negative four happened on this problem so it’s my first time doing it I didn’t like we rehearsed the problem breathing I probably work this out about a year ago so it’s interesting we got 1/8 in an interesting a how pretty the answers look okay so this is our four and then same thing 16 + 16 16 + 16 really nice so this case we also get for 4/32 o that’s really cool we got the same exact answer kind of nice right kind of nice I to hope this video has been helpful to anyone out there who is learning some stuff with **derivative of arctan(y/x)**.

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]]>Nested inside the arc tan function, which means that we can use chain rule in order to do that. We’re going to say u equals 2x. Then rewrite the whole equation. So dy/dx going to equal d/dx of arc tangent of u. And then since we are differentiating with respect to x of it the function in terms of U ran after you chain rule.

Let’s rewrite that using chain rule dy/dx equals.u of arc tangent. Trans issues and we know appear that you equals 2x so taking the derivative of both sides we get du/dx is equal to 2. So do you think Jack’s equal to 2x derivative of arctan of you with respect to U. We already solved that in the derivative. So, we have one over 1 / U squared + 1 and then we have one final line to write. That’s going to be dy/dx equals 2 * 1 is equal to 132 over. You is to act so we have two x squared. plus one and what’s actually might actually take one more line and multiply out this exponent so if dy/dx is equal to 2 over 4x squared + 1. We are finished.

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]]>Hey, guys, I’m gonna show you. How to find the derivative arctan/tan-inverse of X.

y = tan−1 x

tan y = tan(tan−1 x)

tan y = x

So, we’re gonna

Let, the derivative of y = arctan of x

y’ = 1/(1+x^{2})

and now we apply the function of tan to both sides to get tan y equals

tan of arctan of X but tan and arctan

inverse functions. So, they cancel out so,

we get tan of y equals x and now we want

to implicitly differentiate so the

derivative of tan is sec2 this is

y. and then we use a chain rule so the

derivative of Y is dy/dx and this equals 1 So, let’s rearrange for dy/dx this

equals 1 over second square. I’m just

gonna write something here do the

derivative equals x squared of Y. But we want to find the derivative of arctan of x in terms of X’s at the moment we’ve got away but here we’ve got a relationship that expresses Y’s in terms of X’s so we want to express sec

of Y in terms of tan away and then we

can substitute in for X so we know that

sine squared of y plus cosine is going

to y equals 1 but if we divide every

single term by cos squared away we’re

gonna get tan squared y plus 1 equals

SEC squared of Y and this is another

identity so now we can substitute in for

sec^{2} so this is gonna equal 1 over tan^{2} of y+1 and we know

that tan of y= x so the last step

is substitute in Y so this gives us 1 over x+1 so there you go the derivative of arctan of X.

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