# How can you Differentiate (√x^3+ csc) ..?

May 1, 2018

The derivative is $3 \frac{\sqrt{x}}{2} - \cot \left(x\right) \csc \left(x\right)$

#### Explanation:

The derivative of the given function is the sum of the derivatives of
${x}^{\frac{3}{2}} \mathmr{and} \csc \left(x\right)$.
Note that ${\sqrt{x}}^{3} = {x}^{\frac{3}{2}}$
By the Power Rule, the derivative of the first is:
$\frac{3}{2} \times {x}^{\frac{3}{2} - 1} = 3 \frac{\sqrt{x}}{2}$

The derivative of $c s x \left(x\right) i s - \cot \left(x\right) \csc \left(x\right)$

So the derivative of the given function is $3 \frac{\sqrt{x}}{2} - \cot \left(x\right) \csc \left(x\right)$.