Question

What is the derivative of1/root x​

Answer 1

Answer:

$-\frac{1}{2}$ $x^{-\frac{3}{2}}$

Explanation:

Task: To find the derivative of 1/rootx

Rewrite: To find the derivative of the function 1 / $\sqrt{x}$

To find the derivative, follow these steps:

(i) Rewrite the function as

=> $\frac{1}{\sqrt{x} }$

Remember that $\sqrt{x}$ can be written as $x^{\frac{1}{2} }$

=> $\frac{1}{x^{\frac{1}{2} } }$

=> $x^{-\frac{1}{2} }$

(ii) Multiply the coefficient of $x^{-\frac{1}{2} }$ by the power of $x^{-\frac{1}{2} }$

Coefficient of $x^{-\frac{1}{2} }$ = 1

Power of $x^{-\frac{1}{2} }$ = $-\frac{1}{2}$

=> ($-\frac{1}{2}$ x 1)$x^{-\frac{1}{2} }$

=>  ($-\frac{1}{2}$ )$x^{-\frac{1}{2} }$

=>  $-\frac{1}{2}$ $x^{-\frac{1}{2} }$

(iii) Subtract 1 from the power of  $x^{-\frac{1}{2} }$

=>  $-\frac{1}{2}$ $x^{(-\frac{1}{2} - 1 )}$

=>  $-\frac{1}{2}$ $x^{-\frac{3}{2}}$

Therefore, the derivative of 1/root x is $-\frac{1}{2}$ $x^{-\frac{3}{2}}$