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ruslelena [56]
2 years ago
6

What is the derivative of1/root x​

English
1 answer:
Marina86 [1]2 years ago
4 0
<h2><u><em>Answer:</em></u></h2>

-\frac{1}{2} x^{-\frac{3}{2}}<em />

<em />

<em />

<h2><u><em>Explanation:</em></u></h2>

<em>Task</em>: To find the derivative of 1/rootx

<em>Rewrite</em>: To find the derivative of the function 1 / \sqrt{x}

To find the derivative, follow these steps:

<em>(i) Rewrite the function as</em>

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

<em>Remember that </em>\sqrt{x}<em> can be written as </em>x^{\frac{1}{2} }<em />

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

=> x^{-\frac{1}{2} }<em />

<em />

<em>(ii) Multiply the coefficient of </em>x^{-\frac{1}{2} }<em> by the power of </em>x^{-\frac{1}{2} }<em />

Coefficient of x^{-\frac{1}{2} }<em> </em>= 1

Power of x^{-\frac{1}{2} }<em> </em>= -\frac{1}{2}

=> (-\frac{1}{2} x 1)x^{-\frac{1}{2} }<em />

=>  (-\frac{1}{2} )x^{-\frac{1}{2} }<em />

=>  -\frac{1}{2} x^{-\frac{1}{2} }<em />

<em />

<em>(iii) Subtract 1 from the power of  </em>x^{-\frac{1}{2} }<em />

=>  -\frac{1}{2} x^{(-\frac{1}{2} - 1 )}<em />

=>  -\frac{1}{2} x^{-\frac{3}{2}}<em />

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

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