Question

Find the derivative of. y= log e sin x​

Answer 1

Given :-

• Function

$\tt \: y = log_{e}(x) \times \sin \: x$

To Find :-

• We have to find the derivative of the given function.

Formula to be used :-

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

Solution :-

Let $\sf\:u. be =\log_{e}\:x$

Where,

v = Sinx

y = u × v

Now, differentiate with respect to x :-

$\tt \dfrac{dy}{dx} = \sin \: x \times \dfrac{ d\log_{e}(x)}{dx} + \log_{e}(x) \times \dfrac{ d\sin \: x}{dx}$

$\implies \tt \dfrac{dy}{dx} = \sin \: x \times \dfrac{1}{x} + log_{e}(x) \times \cos \: x$

$\implies \tt \dfrac{dy}{dx} = \dfrac{ \sin \:x}{x} + \log_{e}(x) \times \cos \: x$