Question

differentiate the function 1/√x​

Answer 1

Answer:

f'(x)=−12x32

Explanation:

Remember that ddx[xn]=nxn−1.

We can rewrite the f(x) so that f(x)=1x12=x−12.

Using the aforementioned rule, we know that f'(x)=−12x−32.

We can rewrite this as f'(x)=−12x32.

Answer 2

$\frac{dy}{dx} \: = \frac{d}{dx} x ^{ \frac{ - 1}{2} } = \frac{ - 1}{2} \times {x}^{ \frac{ - 1}{2} - 1} = \frac{ - 1}{2} \times {x}^{ - \frac{ 3}{2} } = \frac{ - 1}{2 (\sqrt{x})^{3} }$