If y -sin x and x -3 t- then dy - dt will beA- cos xB- 9 cos xC- -cos xD- 3 cos 3 t

The correct option is D 3 cos⁡(3t)y=sin⁡x and x=3t dydx=cos⁡x and dxdt=3 dydt=dydx×dxdt=3 cos⁡x=3 cos⁡(3t) Alternative: Replace the value of x in sin⁡x by 3 ...

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Byju's Answer

Standard XII

Physics

Chain Rule of Differentiation

If y =sin x a...

Question

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

9 cos x

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cos x

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3 cos (3 t)

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- cos x

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Solution

The correct option is C $3 cos (3 t)$
$y = sin x$ and $x = 3 t$

$\frac{d y}{d x} = cos x$ and $\frac{d x}{d t} = 3$

$\frac{d y}{d t} = \frac{d y}{d x} \times \frac{d x}{d t} = 3 cos x = 3 cos (3 t)$

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

$\frac{d y}{d t} = 3 cos (3 t)$

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If y=sinx and x=3t, then dydt will be

The correct option is C 3cos(3t)y=sinx and x=3t dydx=cosx and dxdt=3 dydt=dydx×dxdt=3cosx=3cos(3t) Alternative: Replace the value of x in sinx by 3t y=sin(3t) dydt=3cos(3t)

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