How do you differentiate g(x)=sqrtxe^x?

1 Answer
Monzur R.
Dec 27, 2016

g'(x)=e^x(1/(2sqrt(x))+sqrt(x))

Explanation:

g(x)=sqrt(x)e^x=(x)^(1/2)e^x

u=(x)^(1/2), v=e^x

g'(x)=vu'+uv'

u'=1/2x^(-1/2)=1/(2sqrt(x)), v'=e^x

g'(x)=e^x/(2sqrt(x))+sqrt(x)e^x=e^x(1/(2sqrt(x))+sqrt(x))

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