Question

if y=x sin x find dy/dx​

Answer 1

Given :-

y=x sin x

To find :-

dy/dx

Solution :-

➜ y=x sin x

Differentiating both sides :-

➜ dy/dx = d(x sin x)/dx

➜ dy/dx = [d(x)/dx ] sin x + x [d(sin x)/dx ]

➜ dy/dx = sin x + x cos x

Answer :-

dy/dx = sin x + x cos x

Additional Information :-

d(e^x)/dx = e^x

d(x^n)/dx = n x^(n-1)

d(ln x)/dx = 1/x

d(sin x)/dx = cos x

d(cos x)/dx = - sin x

d(tan x)/dx = sec² x

d(sec x)/dx = tan x * sec x

d(cot x)/dx = - cosec²x

d(cosec x)/dx = - cosec x * cot x

Answer 2

Answer:

$y = x \sin \: x$

$\frac{dy}{dx} = \frac{d(x)}{dx} \sin \: x + x \frac{d( \sin \: x)}{dx}$

$\frac{dy}{dx} = \sin \: x + x \cos \: x$