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

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

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

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

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

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