Question

Find the derivative of given function w.r.t. the independent variable x.
1)xsinx

plzz solve this​

Answer 1

Refer the attachment

#RITZ

Answer 2

The derivative of xsinx with respect to the independent variable x is sinx + xcosx

Given :

The function xsinx

To find :

The derivative of xsinx with respect to the independent variable x

Formula :

$\displaystyle \sf{ \frac{d}{dx} (uv) =u \frac{dv}{dx} + v\frac{du}{dx} }$

Solution :

Step 1 of 2 :

Write down the given function

Let f(x) be the given function

Then f(x) = xsinx

Step 2 of 2 :

Find derivative of xsinx with respect to the independent variable x

f(x) = xsinx

Differentiating both sides with respect to x we get

$\displaystyle \sf{ \frac{d}{dx} (f(x)) = \frac{d}{dx}(xsinx) }$

$\displaystyle \sf\implies f'(x) = x \frac{d}{dx}(sinx) + sinx\frac{d}{dx}(x)\: \: \: \bigg[ \because \: \frac{d}{dx} (uv) =u \frac{dv}{dx} + v\frac{du}{dx}\bigg]$

$\displaystyle \sf\implies f'(x) = x. cosx + sinx. 1$

$\displaystyle \sf\implies f'(x) = x \: cosx + sinx$

Hence the derivative of xsinx with respect to the independent variable x is sinx + xcosx

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