Question

formulas for differentiation of inverse function .​

Answer 1

Answer:

dydx=ddx(f−1(x))=(f−1)′(x)=1f′(f−1(x)). g′(x)=1f′(g(x)). Use the inverse function theorem to find the derivative of g(x)=x+2x. Compare the resulting derivative to that obtained by differentiating the function directly

Hope it helps

Answer 2

Answer:

The Derivative of an Inverse Function.

(f−1)′(a)=pq. f′(f−1(a))=qp. (f−1)′(a)=1f′(f−1(a)).

Finding the Inverse of a Function

• First, replace f(x) with y . ...
• Replace every x with a y and replace every y with an x .
• Solve the equation from Step 2 for y . ...
• Replace y with f−1(x) f − 1 ( x ) . ...
• Verify your work by checking that (f∘f−1)(x)=x ( f ∘ f − 1 ) ( x ) = x and (f−1∘f)(x)=x ( f − 1 ∘ f ) ( x ) = x are both true