How do you differentiate #f(x) = x^3sqrt(7x+1)# using the product rule?

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Answer 1 · 2017-04-13T21:58:24

#f'(x)=3x^2sqrt(7x+1)+(7x^3)/(2sqrt{7x+1})#

By rewriting a bit,

#f(x)=x^3(7x+1)^(1/2)#

#f'(x)=3x^2 cdot (7x+1)^(1/2)+x^3 cdot1/2(7x+1)^(-1/2)(7)#

By cleaning up a bit,

#=3x^2sqrt(7x+1)+(7x^3)/(2sqrt{7x+1})#

I hope that this was clear.