6. Derivatives of Inverse, Exponential, & Logarithmic Functions

Which of the following is the correct derivative of $y=arcsin\left(x\right)$ with respect to $x$?

In Exercises 25–36, find the derivative of y with respect to the appropriate variable.

27. y = (1 - θ)tanh⁻¹(θ)

Find the derivative of the given function.

$f(x)=(x^3+4x)\sin^{-1}x$

Find the derivative of the given function.

$y=4\arccos\left(3x^6-x^5\right)$

Find the derivative of the given function.

$f(x)=\tan^{-1}(x^2)$