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First Fundamental Theorem of Calculus

If x=3t and y...

Question

If $x = 3 t$ and $y = t^{3},$ then $\frac{d y}{d x}$ at $t = 1$ is equal to

A

\frac{1}{3}

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B

1

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C

2

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D

- 1

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Solution

The correct option is B $1$
We have,
$x = 3 t$
$\Rightarrow \frac{d x}{d t} = 3$
and, $y = t^{3}$
$\Rightarrow \frac{d y}{d t} = 3 t^{2}$
$∴ \frac{d y}{d x} = \frac{\frac{d y}{d t}}{\frac{d x}{d t}}$
$\Rightarrow \frac{d y}{d x} = \frac{3 t^{2}}{3} = t^{2}$
At $t = 1,$
$\frac{d y}{d x} = 1$

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