Question

If y=xsinx,then find dy/dx

Answer 1

y=xsinx
dy/dx=x d/dx xsinx +sinx d/dx(x)
dy/dx=xcosx+sinx

Answer 2

$\bold{\frac{d y}{d x}=x \cos x+\sin x}$

The given equation is to be differentiated in terms of y with respect to x.

Given Equation: y = x sin x  

${d \frac{y}{d x}=d \frac{(x \sin x)}{d x}}\\ {d \frac{y}{d x}=x \frac{d(\sin x)}{d x}+\sin x\ d \frac{x}{d x}}$

$\begin{array}{c}{d \frac{y}{d x}=x \cdot \cos x+\sin x \cdot 1} \\ {d \frac{y}{d x}=x \cos x+\sin x}\end{array}$

The value of y by differentiating in terms of y with respect to x $d \frac{y}{d x}=x \cos x+\sin x.$