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How do you differentiate #f(x)=cos(e^(x^4)) # using the chain rule?

1 Answer

Shwetank Mauria

Jun 18, 2016

#(df)/(dx)=-4x^3e^(x^4)sin(e^(x^4))#

Explanation:

Here #f(x)=cos(g(x))#, where #g(x)=e^(h(x))# and #h(x)=x^4#

Hence, using chain rule

#(df)/(dx)=-sin(e^(x^4))xxe^(x^4)xx4x^3#

or #(df)/(dx)=-4x^3e^(x^4)sin(e^(x^4))#

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