How do you differentiate # f(x)= sqrt((xe^x+4)^3 # using the chain rule.?

Question

1338 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-30T20:12:29

#f'(x)=3/2e^x(1+x)(sqrt(xe^x+4))#

#f(x)=sqrt((xe^x+4)^3)=((xe^x+4)^(3))^(1/2))=(xe^x+4)^(3/2)#

#[f(x)]^n=n[f(x)]^(n-1)xxf'(x)#

#d/dxuv=uv'+vu'#

#f'(x)=3/2(xe^x+4)^(1/2)xx(e^x+xe^x)=#

#3/2e^x(1+x)sqrt(xe^x+4)#