Let y=t^ 10 +1 and x=t^8+1, then d^2 y d x^2 is equal to - Vidyadip

MCQ

Let $y=t^{10}+1$ and $x=t^8+1$, then $\frac{d^2 y}{d x^2}$ is equal to

A
$\frac{5}{2} t$
✓
$\frac{5}{16 t^6}$
C
$20 t^8$
D
None of these

✓

Answer

Correct option: B.

$\frac{5}{16 t^6}$

We have, $y=t^{10}+1, x=t^8+1$
$\Rightarrow \frac{d y}{d t}=10 t^9, \frac{d x}{d t}=8 t^7$
$\therefore \frac{d y}{d x}=\frac{d y / d t}{d x / d t}=\frac{10 t^9}{8 t^7}=\frac{5}{4} t^2$
$\Rightarrow \frac{d^2 y}{d x^2}=\frac{5}{4}(2 t) \frac{d t}{d x}$
$=\frac{5}{4} \times 2 t \times \frac{1}{8 t^7}$
$=\frac{5}{16 t^6}$

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