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

$\left(\setminus \frac{1 - 2 x}{2 \setminus \sqrt{x}}\right) \setminus \sin x + \left(\setminus \frac{1 + 2 x}{2 \setminus \sqrt{x}}\right) \setminus \cos x$

#### Explanation:

Differentiating given function: $f \left(x\right) = \setminus \sqrt{x} \left(\setminus \sin x + \setminus \cos x\right)$ w.r.t. $x$ using product rule as follows

$f ' \left(x\right) = \frac{d}{\mathrm{dx}} \left(\setminus \sqrt{x} \left(\setminus \sin x + \setminus \cos x\right)\right)$

$= \setminus \sqrt{x} \frac{d}{\mathrm{dx}} \left(\setminus \sin x + \setminus \cos x\right) + \left(\setminus \sin x + \setminus \cos x\right) \frac{d}{\mathrm{dx}} \setminus \sqrt{x}$

$= \setminus \sqrt{x} \left(\setminus \cos x - \setminus \sin x\right) + \left(\setminus \sin x + \setminus \cos x\right) \frac{1}{2 \setminus \sqrt{x}}$

$= \left(\setminus \frac{1 - 2 x}{2 \setminus \sqrt{x}}\right) \setminus \sin x + \left(\setminus \frac{1 + 2 x}{2 \setminus \sqrt{x}}\right) \setminus \cos x$