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If #f(x) = 4x -2# and #g(x) = e^(-x^3-1)#, what is #f'(g(x)) #?

1 Answer

A. S. Adikesavan

Apr 30, 2016

#12x^2e^(-x^3-1)=(12/e)x^2e^(-x^3)#.

Explanation:

#f(g(x)=4g(x)-1=4e^(-x^3-1)-2#

Use #(e^u)'=(e^u)u'#.

#f'(g(x)) =(4e^(-x^3-1)-2)'=4(e^(-x^3-1))'=4e^(-x^3-1)(-x^3-1)'=4e^(-x^3-1)(3x^2)=(12/e)x^2e^(-x^3)#

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