First slide

Derivatives

Question

$If y = f (\frac{5 x + 1}{10 x^{2} - 3}) and f^{'} (x) = \cos x then \frac{d y}{d x} =$

Moderate

A

$\cos (\frac{5 x + 1}{10 x^{2} - 3}) \frac{d}{d x} (\frac{5 x + 1}{10 x^{2} - 3})$
B

$\frac{5 x + 1}{10 x^{2} - 3} \cos (\frac{5 x + 1}{10 x^{2} - 3})$
C

$\cos (\frac{5 x + 1}{10 x^{2} - 3})$
D

none of these

Solution

$\begin{array}{l} let t = \frac{5 x + 1}{10 x^{2} - 3} \Rightarrow y = f (t) \\ \frac{d y}{d x} = f^{'} (t) \frac{d t}{d x} [∵ f^{'} (x) = \cos x] \\ \frac{d y}{d x} = \cos (\frac{5 x + 1}{10 x^{2} - 3}) \frac{d}{d x} (\frac{5 x + 1}{10 x^{2} - 3}) \end{array}$

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