For differentiable functions ,

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

For differentiable functions ff, gg, and hh, let y=f(g(h(x)))y = f\bigl(g\bigl(h(x)\bigr)\bigr). Which of the following expressions equals dydx\dfrac{dy}{dx}? (a) f′(g(h(x))) g′(h(x))f'(g(h(x)))\,g'(h(x)) (b) f′(g(x)) g′(h(x)) h′(x)f'(g(x))\,g'(h(x))\,h'(x) (c) f′(g(h(x))) g′(h(x)) h′(x)f'(g(h(x)))\,g'(h(x))\,h'(x) (d) f′(g(h(x))) g′(x) h′(x)f'(g(h(x)))\,g'(x)\,h'(x)

Related theory

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