In Exercises 21–48, find the derivative of y with respect to t...

Question

In Exercises 21–48, find the derivative of y with respect to the appropriate variable.

33. y=ln(arctan(x))

Accepted Answer

Welcome back everyone. Find the derivative of y with respect to x if y equals ln of inverse of tangent of 3 x. So for this problem, we want to find D Y divided by DX and we have to notice that Y is a composite function. So first of all, we're going to differentiate the outer function, LN of inverse of tangent. Of 3 x with respect to the middle function. So in this case that would be inverse of tangent of 3 x. We are going to multiply by the derivative of the middle function. So the derivative of inverse of tangent of 3 x with respect to the inner function that would be 3 x. And finally we want to multiply by the derivative of the inner function 3 x with respect to x. So the derivative of the natural logarithm is going to be 1 divided by the inner function, so in this case one divided by inverse of tangent. Of 3 eggs The derivative of inverse of tangent is going to be 1 divided by 1 plus the square of the inner function, so 1 + 3 x squared, and the derivative of 3 x is 3 because the derivative of x is a 1. So now we want to simplify. We are going to get 3. Divided by 1 + 9 x 2 Multiplied by inverse of tangent of 3 x, and that's our final answer for this problem. Thank you for watching.

In Exercises 21–48, find the derivative of y with respect to the appropriate variable.33. y=ln(arctan(x))

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In Exercises 21–48, find the derivative of y with respect to the appropriate variable.
33. y=ln(arctan(x))