Derivative of inverse of f(x)=e^(-2x)-9x^3+4 at point (0,5)?

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Answer 1 · 2018-07-07T01:36:09

#-1/2#

Derivative of #f(x)# :

#f^'(x) = d/dx(e^(-2x)-9x^3+4) = -2e^(-2x)-27x^2#

Thus

#f^'(0) = -2#

Let #g# be the inverse of #f#. Then

#g(f(x)) = x#

Using the chain rule, we get

#g^'(f(x)) times f^'(x) = 1 implies#

#g^'(f(0))times (-2)=1 implies#

#g^'(5) = -1/2#