Let and be differentiable functions

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

Let y=f(u)y=f(u) and u=g(x)u=g(x) be differentiable functions. Which of the following relations is correct when expressing dydx\dfrac{dy}{dx} entirely in Leibniz notation? (a) dydx=dydu+dudx\displaystyle\frac{dy}{dx}=\frac{dy}{du}+\frac{du}{dx} (b) dydx=dudy⋅dxdu\displaystyle\frac{dy}{dx}=\frac{du}{dy}\cdot\frac{dx}{du} (c) dydx=dydu⋅dudx\displaystyle\frac{dy}{dx}=\frac{dy}{du}\cdot\frac{du}{dx} (d) dydx=dydx⋅dudx\displaystyle\frac{dy}{dx}=\frac{dy}{dx}\cdot\frac{du}{dx}

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