Question

How do I differentiate f(x)=xcosx+2tanx

Answer 1

d/dx(xcosx)+d/dx(2tanx)
= (1*cosx + x*(-sinx) + 2sec^2(x)
= cosx - xsinx + 2sec^2(x)

Answer 2

`(dy)/(dx)=\cos x-x\sin x+2\sec^2x`

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,

`(dy)/(dx)=(d(x\cos x))/(dx)+(d(2\tan x))/(dx)`

Apply product rule,
`(d)/(dx)(u\cdot v)=u'v+v'u`

`(dy)/(dx)=(d)/(dx)(\cos x)x+\cos x(d)/(dx)(x)+2\sec^2x`

`(dy)/(dx)=-x\sin x+\cos x+2\sec^2x`

Therefore,
`(dy)/(dx)=\cos x-x\sin x+2\sec^2x`