Question

How do you differentiate `sqrtx(sinx+cosx)`?

Answer 1

`(\frac{1-2x}{2\sqrtx})\sin x+(\frac{1+2x}{2\sqrtx})\cos x`

Explanation:

Differentiating given function: `f(x)=\sqrtx(\sinx +\cosx )` w.r.t. `x` using product rule as follows

`f'(x)=d/dx(\sqrtx(\sinx +\cosx ))`

`=\sqrtxd/dx(\sin x+\cos x)+(\sin x+\cos x)d/dx\sqrtx`

`=\sqrtx(\cos x-\sin x)+(\sin x+\cos x)1/{2\sqrtx}`

`=(\frac{1-2x}{2\sqrtx})\sin x+(\frac{1+2x}{2\sqrtx})\cos x`