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## 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 $$g'(6)?$$

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