6. Derivatives of Inverse, Exponential, & Logarithmic Functions

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.

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

Find the derivative of the given function.

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

Find the derivative of the given function.

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

Find the slope of the line tangent to the graph of y = sin^−1 x at x=0.

Find the slope of the line tangent to the graph of y = tan^−1 x at x= −2.