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3 years ago

(Citizenship 02.03 HC)

English

1 answer:

erma4kov [3.2K]3 years ago

3 0

Lol I would search it on google

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3 years ago

What is the derivative of1/root x

Marina86 [1]

<h2>Answer:</h2>

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

<h2>Explanation:</h2>

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

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3 years ago