Question

if y =xsinx^2 then the value of dy/dx is ​

Answer 1

Answer:

option 1 is right....

hope it helps you

Answer 2

The value of $\frac{dy}{dx}$ is $sinx^{2} +2x^{2} cosx^{2}$   and option(1) is correct.

Step-by-step explanation:

Given:

Function $y=x \ sinx^{2}$.

To Find:

The value of $\frac{dy}{dx}$.

Formula Used:

Function y = uv,      where u and v are the functions of x.

$\frac{dy}{dx} = u\frac{dv}{dx} + v\frac{du}{dx}$  --------------- formula no.01.

The above is  product rule of differentiation.

Solution:

As given- function $y=x \ sinx^{2}$.

Considering $u=x$  and $v=sinx^{2}$

Applying formula no.01.

$\frac{dy}{dx} = u\frac{dv}{dx} + v\frac{du}{dx}$

$\frac{dy}{dx} = x\frac{d(sinx^{2} )}{dx} + sinx^{2} \frac{d(x)}{dx}$

    $= x\times cosx^2 \times\frac{d(x^{2} )}{dx} +sinx^{2} \times1$

    $= x\times cosx^2 \times2x+sinx^{2}$

    $= 2x^{2} cosx^2 +sinx^{2}$

Thus,the value of $\frac{dy}{dx}$ is $sinx^{2} +2x^{2} cosx^{2}$   and option(1) is correct.

PROJECT CODE #SPJ3