Find the derivative of this function?

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Answer 1 · 2017-04-24T17:51:35

Looks like an invite to use the Quotient Rule but I'd re-write and do this:

#= d/dx ( e^(x^3) cos^3 (x^3) )#

#= d/dx ( e^(x^3) ) cos^3 (x^3) + e^(x^3)d/dx (cos^3 (x^3) )#

Lots of Chain Rule here:

#= (3 x^2 cdot e^(x^3)) cos^3 (x^3) + e^(x^3)( 3 cos^2 (x^3) cdot ( - sin (x^3)) cdot 3 x^2)#

And gather terms:

#=3x^2 e^(x^3) cos^2 x^3 ( cos x^3 - 3 sin x^3 ) #