Question

Differentiate xcos2x.derivative of xcos2x is =?

Accepted Answer

We have to differentiate f(x) = x*cos 2x
f'(x) = x'*cos 2x + x*(cos 2x)'
f'(x) = cos 2x + x*(-sin 2x)*2
f'(x) = cos 2x - 2x*(sin 2x)
The required derivative of f(x) = x*cos 2x is f'(x) = cos 2x - 2x*(sin 2x)

Answer

Let y = x*cos2x
We'll apply the chain rule and also the product rule.
dy/dx = [d/dx(x)]* cos2x + x* [d/dx (cos 2x)]
We'll apply the chain rule for the term:
[d/dx (cos 2x)] = -sin 2x* (2x)'
[d/dx (cos 2x)] = -2sin 2x
The differentiated given function is: dy/dx =  cos 2x - 2x(sin 2x)

Calculus

Differentiate xcos2x. derivative of xcos2x is =?

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