If x^p y^q = (x + y)^ p + q , then d^2 y d x^2 = - Vidyadip

MCQ

If ${x^p}{y^q} = {(x + y)^{p + q}}$, then $\frac{{{d^2}y}}{{d{x^2}}} = $

✓
$0$
B
$1$
C
$2$
D
None of these

✓

Answer

Correct option: A.

$0$

a
(a) Taking $\log $ and differentiating, we get $x\frac{{dy}}{{dx}} - y = 0$
Differentiating again, we get $\frac{{{d^2}y}}{{d{x^2}}} = 0$.

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 $f(x)=x^2+4 x-5$ and $A=\left|\begin{array}{ll}1 & 2 \\ 4 & -3\end{array}\right|$, then $f(A)$ is equal to

If $ \displaystyle \begin{vmatrix} 2 &\text{amp;} -4 \\ 9 &\text{amp; d}-3 \end{vmatrix}=4$ then $\text{d}=$

The radius of a circle is increasing at the rate of $0.4 \ cm/ s.$ The rate of increasing of its circumference is:

Set $A$ has $3$ elements, and set $B$ has $4$ elements. Then the number of injective mappings that can be defined from $A$ to $B$ is:

If $N$ be the set of all$-$natural numbers, consider $f : N \rightarrow N$ such that $f(x) = 2x, \forall x \in N,$ then $f$ is:

The area of the region bounded by $y^{2}=8 x$ and $y^{2}=16(3-x)$ is equal to

The function $f(x)=\cot x$ is discontinuous on the set

The integrating factor of the differential equation $x \frac{d y}{d x}+2 y=x^2$ is

Let $A$ and $B$ be two independent events such that $\mathrm{P}(\mathrm{A})=\frac{1}{3}$ and $\mathrm{P}(\mathrm{B})=\frac{1}{6} .$ Then, which of the following is TRUE?

$\int_0^1 {\log \sin \left( {\frac{\pi }{2}x} \right)} \,dx = $