Question

If $y=\sin x$ and $x=3t$, then $\frac{dy}{dt}$ will be

• A. $9\cos x$
• B. $\cos x$
• C. $3\cos \left(3t\right)$
• D. $-\cos x$

Answer 1

The correct option is C $3\cos \left(3t\right)$

$y=\sin x$ and $x=3t$

$\frac{dy}{dx}=\cos x$ and $\frac{dx}{dt}=3$

$\frac{dy}{dt}=\frac{dy}{dx}\times \frac{dx}{dt}=3\cos x=3\cos \left(3t\right)$

Alternative:
Replace the value of $x$ in $\sin x$ by $3t$
$y=\sin \left(3t\right)$

$\frac{dy}{dt}=3\cos \left(3t\right)$