For differentiable functions and with

MATHEMATICS · Single correct · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

For differentiable functions

x=f(t)

and

y=g(t)

with

f'(t)\neq0

, which of the following expressions equals

\dfrac{d^{2}y}{dx^{2}}

in terms of derivatives with respect to

t

? (a)

\dfrac{g''(t)\,f'(t)-g'(t)\,f''(t)}{[f'(t)]^{2}}

(b)

\dfrac{g''(t)\,f'(t)+g'(t)\,f''(t)}{[f'(t)]^{3}}

(c)

\dfrac{f'(t)\,g''(t)-g'(t)\,f''(t)}{[f'(t)]^{3}}

(d)

\dfrac{g'(t)\,f''(t)-g''(t)\,f'(t)}{[f'(t)]^{3}}