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 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.

How are the derivatives of sin^−1 x and cos^−1 x related?

Tangent lines Find an equation of the line tangent to the graph of f at the given point.

f(x) = sin⁻¹(x/4); (2,π/6)