How do you differentiate #g(u) =(u^-2 + u^-3)(u^5 - 2u^2) # using the product rule?

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Answer 1 · 2018-01-02T12:44:05

#3u^2+2u+2/u^2#

The product rule states that

#d/dx(ab)=a'b+ab'#

Let #a=u^-2+u^-3#, #b=u^5-2u^2#

#:. g'(u)=(u^-2+u^-3)'(u^5-2u^2)+(u^-2+u^-3)(u^5-2u^2)'#

#g'(u)=(-2/u^3-3/(u^4))(u^5-2u^2)+(u^-2+u^-3)(5u^4-4u)#

#g'(u)=-2u^2+4/u-3u+6/u^2+5u^2+5u-4/u-4/u^2#

#g'(u)=3u^2+2u+2/u^2#