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Basic Differentiation Rule

If y=sin⁡x an...

Question

If $y = s i n x$ and $x = 3 t$ , then $d y / d t$ will be

A

9 c o s x

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B

c o s x

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C

3 c o s 3 t

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D

- c o s x

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Solution

The correct option is C $3 c o s 3 t$

$y = s i n x$ , $x = 3 t$
$\frac{d y}{d x} = c o s x$ , $\frac{d x}{d t} = 3$
$\frac{d y}{d t} = \frac{d y}{d x} \times \frac{d x}{d t} = 3 c o s x = 3 c o s (3 t)$

Alternative:
Replace the value of $x$ in $s i n x$ by $3 t$
$y = s i n (3 t)$
$d y / d t = 3 c o s (3 t)$

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