First slide

Diffrentiation

Question

Given, $y = 3 x^{3}$ Find the value of $\frac{d y}{d t} .$

Moderate

A

$3 x^{2} (\frac{d x}{d t})$
B

$9 x^{3} (\frac{d x}{d t})$
C

$3 x^{3} (\frac{d x}{d t})$
D

$9 x^{2} (\frac{d x}{d t})$

Solution

$\frac{d y}{d t} = (\frac{d y}{d x}) (\frac{d x}{d t}) = [\frac{d}{d x} (3 x^{3})] \frac{d x}{d t} = 9 x^{2} (\frac{d x}{d t})$

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