Waste less time on Facebook — follow Brilliant.
×

Differentiation Rules

These are the rules that explain how to take derivatives of any functions: from polynomials to trigonometric functions to logarithms.

Inverse Function Rule

Given the function \(f(x)=3x^2+2x+1,\) what is the value of \(\left(f^{-1}\right)'(6)?\)

Given the function \(f(x)=5\ln\frac{x}{4},\) what is the value of \(\left(f^{-1}\right)'(\ln32)?\)

If \(f(x)=5\sin^{-1}3x,\) what is the value of \(f'\left(\frac{\sqrt{3}}{6} \right)?\)

Given \(f(x)=5x+\frac{1}{x},\) what is \(\left(f^{-1}\right)'(6)?\)

Let \(f(x)\) be a differentiable function and let \(g(x)\) be the inverse of \(f(x)\). If \(f(2)=6\) and \(f'(2)=\frac{1}{5},\) what is the value of \(g'(6)?\)

×

Problem Loading...

Note Loading...

Set Loading...