#### To determine

**To find:** The differentiation of f(x)=x2sinx.

#### Answer

The differentiation of f(x)=x2sinx is x2cosx+2xsinx_.

#### Explanation

**Given:**

The function is, f(x)=x2sinx.

**Formula used:**

**Product Rule:**

The product rule for two functions f1(x) and f2(x) is given as follows*.*

ddx[f1(x)f2(x)]=f1(x)⋅ddx[f2(x)]+f2(x)⋅ddx[f1(x)] (1)

**Power Rule:**

If *n* is a real number, then the power rule is,

ddx(xn)=nxn−1 (2)

**Calculation:**

Substitute x2 for f1(x) and sinx for f2(x) in equation (1).

ddx(x2sinx)=x2⋅ddx(sinx)+sinx⋅ddx(x2)

Apply Power Rule as shown in equation (2).

ddx(x2sinx)=x2⋅(cosx)+sinx⋅(2x2−1)=x2⋅(cosx)+sinx⋅(2x)=x2cosx+2xsinx

Therefore, the differentiation of f(x)=x2sinx is x2cosx+2xsinx_.