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Derivation of Inverse Function Without Finding the Inverse and Derivation of Formula
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#InverseFunctions #InverseDerivatives #Calculus
Derivative of Inverse Functions: Inverse function has reciprocal slope at corresponding points.
Prove
(f^(-1) )'(x)=1/(f^' (f^(-1) (x)) )
Application
Verify that f(x) has an inverse. Then use the function f and the given real number a to find (f^(-1) )^' (a)
Q1. f(x)=2x^3+4, find (f^(-1) )^' (a),a=20
Q2. f(x)=x^5-x^3+2x
(f^(-1) )^' (a),a=2
Derivative of Inverse Functions: Inverse function has reciprocal slope at corresponding points.
Prove
(f^(-1) )'(x)=1/(f^' (f^(-1) (x)) )
Application
Verify that f(x) has an inverse. Then use the function f and the given real number a to find (f^(-1) )^' (a)
Q1. f(x)=2x^3+4, find (f^(-1) )^' (a),a=20
Q2. f(x)=x^5-x^3+2x
(f^(-1) )^' (a),a=2
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