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Calculus

Differentiation Rules

Differentiation of Inverse Functions

         

Given the function \(f(x)=3x^2+2x+1\) defined only for \(x > 0,\) 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 \(f(x)=5x+\frac{1}{x}\) in the domain \( x > \frac{1}{2} ,\) 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 \(g'(6)?\)

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