d^2 x d y^2 = - Vidyadip

MCQ

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

A
$ - {\left( {\frac{{{d^2}y}}{{d{x^2}}}} \right)^{ - 1}}{\left( {\frac{{dy}}{{dx}}} \right)^{ - 3}}$
B
$\;\left( {\frac{{{d^2}y}}{{d{x^2}}}} \right){\left( {\frac{{dy}}{{dx}}} \right)^{ - 2}}$
✓
$ - \left( {\frac{{{d^2}y}}{{d{x^2}}}} \right){\left( {\frac{{dy}}{{dx}}} \right)^{ - 3}}$
D
$\;{\left( {\frac{{{d^2}y}}{{d{x^2}}}} \right)^{ - 1}}$

✓

Answer

Correct option: C.

$ - \left( {\frac{{{d^2}y}}{{d{x^2}}}} \right){\left( {\frac{{dy}}{{dx}}} \right)^{ - 3}}$

c
$\frac{{{d^2}x}}{{d{y^2}}} = \frac{d}{{dy}}\left( {\frac{{dx}}{{dy}}} \right) = \frac{d}{{dy}}\left( {\frac{1}{{\frac{{dy}}{{dx}}}}} \right)$

$ = \frac{d}{{dx}}\left( {\frac{1}{{\frac{{dy}}{{dx}}}}} \right) \cdot \frac{{dx}}{{dy}} = - \frac{1}{{{{\left( {\frac{{dy}}{{dx}}} \right)}^2}}} \cdot \frac{{{d^2}y}}{{d{x^2}}} \cdot \frac{1}{{\left( {\frac{{dy}}{{dx}}} \right)}}$

$=-\frac{1}{\left(\frac{d y}{d x}\right)^{3}} \cdot \frac{d^{2} y}{d x^{2}}=-\left(\frac{d y}{d x}\right)^{-3}\left(\frac{d^{2} y}{d x^{2}}\right) $

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from STD 12 - 5. continuity and differentiation→STD 12 - 5. continuity and differentiation — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

If A and B are two events such that $\text{P(A)}=\frac{4}{5},$ and $\text{P}(\text{A}\cap\text{B})=\frac{7}{10},$ then P(B|A) =

$\int_{}^{} {\frac{{dx}}{{\sqrt {1 + x} + \sqrt x }} = } $

If $\sin\text{x}\frac{\text{dy}}{\text{dx}}+\text{y}\cos\text{x}=\text{x}\sin\text{x},$ then $(\text{y}-1)\sin\text{x}=$

An iso$-$profit line represents:

If $|a|\, = 2,\,\,|b|\, = 3$ and $a, b$ are mutually perpendicular, then the area of the triangle whose vertices are $0,\,\,a + b,\,\,a - b$ is

If $\text{y}=\frac{1}{1+\text{x}^{\text{a}-\text{b}}+\text{x}^{\text{c}-\text{b}}}+\frac{1}{1+\text{x}^{\text{b}-\text{c}}+\text{x}^{\text{a}-\text{c}}}+\frac{1}{1+\text{x}^{\text{b}-\text{a}}+\text{x}^{\text{c}-\text{a}}},$ then $\frac{\text{dy}}{\text{dx}}$ is equal to:

The minimum value of the polynomial $x(x + 1) (x + 2) (x + 3)$ is

Range of $\text{f(x)}=\sqrt{(1-\cos\text{x})\sqrt{(1-\cos\text{x})\sqrt{(1-\cos\text{x}).....\infty}}}$

The maximum and minimum values of the function $|\sin 4x + 3|$ are

The direction cosines of the vector $3i - 4j + 5k$ are