Question

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

• A. $\cos\left(\frac{5x +1}{10x^{2} -3}\right) \frac{d}{dx}\left(\frac{5x+1}{10x^{2} -3}\right)$
• B. $\frac{5x +1}{10x^{2} -3} \cos \left(\frac{5x+1}{10x^{2} -3}\right)$
• C. $ \cos \left(\frac{5x+1}{10x^{2} -3}\right)$
• D. none of these

Answer 1

Answer: (A)

Suppose that $t = \frac{5x + 1}{10x^2 - 3}$ , so $y =f(t)$
$\therefore \:\:\: \frac{dy}{dx} =f'\left(t\right). \frac{dt}{dx}$ [Since $ f'\left(x\right) =\cos x $]
$\frac{dy}{dx} =\cos \left(\frac{5x +1}{10x^{2} -3}\right) \frac{d}{dx} \left(\frac{5x+1}{10x^{2} -3}\right)$