# Answer to Question #15568 in Calculus for hsd

Question #15568

Y(u)=(u^−2+u^−3)(u^5−1u^2) Find Y′(u)?

Expert's answer

Let's transform the given statement:

Y(u) = (u^(-2)+u^(-3))*(u^5-1*u^2) = (u+1)/u*(u^3-1)

Then

Y'(u) = (u^3-1)/u-(u+1)(u^3-1)/u^2+3(u+1)u = (3u^4+2u^3+1)/u^2.

Y(u) = (u^(-2)+u^(-3))*(u^5-1*u^2) = (u+1)/u*(u^3-1)

Then

Y'(u) = (u^3-1)/u-(u+1)(u^3-1)/u^2+3(u+1)u = (3u^4+2u^3+1)/u^2.

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