6. Derivatives of Inverse, Exponential, & Logarithmic Functions

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

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)$

Find the derivative of the given function.

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

Find the derivative of the given function.

$f\(\left\)(x\(\right\))=\(\cot\)^{-1}\(\left\)(e^{\(\cos\) x}\(\right\))$

Find the derivative of the given function.

$f(t)=\(\csc\)^{-1}(2t+7)$