📚 How to find the derivative of inverse functions

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What you'll need:

Derivative of inverse: d/dx f^(−1) (x)=1/(f′(f^(−1) (x))) or dy/dx=1/(dx/dy)
Steps:
○ Find the derivative of the function
○ Find the inverse function, if possible
○ Substitute into the formula above

Q. Use the inverse function rule to find the derivative of the inverse for:

a) f(x)=x^6

b) f(x)=3x^(−2)

c) f(x)=x^2+2x+4

d) x=y+y^2+y^3

Q2. The function f has the inverse function f^(−1). If f(−5)=−7 and f^′ (−5)=−8, what is f^(−1)′(−7)?