The general rule for derivate of arctan 2x is here, Let’s take the derivative of arc tangent of 2x. Now we can take the derivative with respect to x of both sides of the equation. So, dy/dx equals d/dx of arc tangent of 2x. Our arctangent of 2x is a function of 2x.
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.