If $x=f(t)$ and $y=g(t)$, then $\frac{d^2 y}{d x^2}$ is equal to

$\frac{g^{\prime \prime}(t)}{f^{\prime \prime}(t)}$

JEE MATHEMATICS MCQ: DIFFERENTIATION

1 Easy

1 of 1

Application +4 | -1

x=f(t)

and

y=g(t)

, then

\frac{d^2 y}{d x^2}

is equal to

View answer and explanation

Correct option: B

\frac{g^{\prime \prime}(t) f^{\prime}(t)-g^{\prime}(t) f^{\prime \prime}(t)}{\left(f^{\prime}(t)\right)^3}

Option B (

\frac{g^{\prime \prime}(t) f^{\prime}(t)-g^{\prime}(t) f^{\prime \prime}(t)}{\left(f^{\prime}(t)\right)^3}

) is correct because it is derived by applying the chain rule and quotient rule to find the second derivative of y with respect to x.

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