Question

If $y=f\left(\frac{5x+1}{10x^2-3}\right)$ and $f^{\prime }(x)=\cos x$ ,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 $y=f(t)$
$\therefore \frac{dy}{dx}=f^{\prime }\left(t\right).\frac{dt}{dx}$ [Since $f^{\prime }\left(x\right)=\cos x$]
$\frac{dy}{dx}=\cos \left(\frac{5x+1}{10x^2-3}\right)\frac{d}{dx}\left(\frac{5x+1}{10x^2-3}\right)$