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Mathematics
20.04.2021 12:43
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How do i differentiate f(x)=xcosx+2tanx

How do i differentiate f(x)=xcosx+2tanx
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mbonilla073
mbonilla073
4,7(71 marks)

\frac{dy}{dx}=\cos x-x\sin x+2\sec^2x

Step-by-step explanation:

Given : Function f(x)=x\cos x+2\tan x

To find : How do I differentiate the function ?

Solution :

Let y=x\cos x+2\tan x

Differentiate w.r.t x,

\frac{dy}{dx}=\frac{d(x\cos x)}{dx}+\frac{d(2\tan x)}{dx}

Apply product rule, \frac{d}{dx}(u\cdot v)=u'v+v'u

\frac{dy}{dx}=\frac{d}{dx}(\cos x)x+\cos x\frac{d}{dx}(x)+2\sec^2x

\frac{dy}{dx}=-x\sin x+\cos x+2\sec^2x

Therefore, \frac{dy}{dx}=\cos x-x\sin x+2\sec^2x

pinolena64
pinolena64
4,5(94 marks)

whats the awnsers

Step-by-step explanation:

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