First slide

Derivatives

Question

$If x = \frac{2}{t^{2}}, y = t^{3} - 1 then \frac{d^{2} y}{d x^{2}} =$

Moderate

A

$15 t^{2}$
B

$\frac{15}{16 t^{2}}$
C

$\frac{15 t^{7}}{16}$
D

$16 t^{2}$

Solution

$\frac{d y}{d x} = \frac{3 t^{2}}{- 4 / t^{3}} = - \frac{3}{4} t^{5} . ∴ \frac{d^{2} y}{d x^{2}} = \frac{- 15}{4} t^{4} \frac{d t}{d x} = - \frac{15}{4} t^{4} \cdot (- \frac{t^{3}}{4}) = \frac{15}{16} t^{7}$

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