What is the derivative of #f(x) = e^-xcos(x^2)+e^xsin(x)#?

1 Answer
Euan S.
Jul 9, 2016

#=-e^(-x)cos(x^2) - 2xe^(-x)sin(x^2) + e^xsin(x) + e^xcos(x)#

Explanation:

Product rule is our friend here.

#d/(dx) (e^(-x)cos(x^2)) + d/(dx)(e^xsin(x))#

#=d/(dx)(e^(-x))cos(x^2) + e^(-x)d/(dx)(cos(x^2)) + d/(dx)(e^x)sin(x) + e^xd/(dx)(sin(x))#

#=-e^(-x)cos(x^2) - 2xe^(-x)sin(x^2) + e^xsin(x) + e^xcos(x)#

NB: for #d/(dx)(cos(x^2))# I have used the chain rule because #x^2# is also a function of x

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