iran-konkur 2013 Q118

iran-konkur · Other · konkur-riazi_1392 3 marks Chain Rule Chain Rule with Composition of Explicit Functions
118- If $f(x) = \dfrac{x^3 - 2}{1 + x^3}$, $g(x) = \sqrt[3]{x-1}$, then $f'(g(x)) \cdot g'(x)$ is equal to which of the following?
(1) $\dfrac{3}{x}$ (2) $\dfrac{3}{x^2}$ (3) $\dfrac{1}{3x}$ (4) $\dfrac{x-3}{x^2}$
118- If $f(x) = \dfrac{x^3 - 2}{1 + x^3}$, $g(x) = \sqrt[3]{x-1}$, then $f'(g(x)) \cdot g'(x)$ is equal to which of the following?

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(1) $\dfrac{3}{x}$ \hfill (2) $\dfrac{3}{x^2}$ \hfill (3) $\dfrac{1}{3x}$ \hfill (4) $\dfrac{x-3}{x^2}$

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