AP

MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

Define y=(x2+4x+7)−32y = (x^{2}+4x+7)^{-\tfrac{3}{2}}. (i) Show that dydx=−32(x2+4x+7)−52(2x+4)\displaystyle \frac{dy}{dx} = -\tfrac{3}{2}(x^{2}+4x+7)^{-\tfrac{5}{2}}(2x+4). (ii) Hence prove that (x2+4x+7) y′=−3(x+2) y(x^{2}+4x+7)\,y' = -3(x+2)\,y.

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