Answer:
[tex]-\frac{1}{2}[/tex] [tex]x^{-\frac{3}{2}}[/tex]
Explanation:
Task: To find the derivative of 1/rootx
Rewrite: To find the derivative of the function 1 / [tex]\sqrt{x}[/tex]
To find the derivative, follow these steps:
(i) Rewrite the function as
=> [tex]\frac{1}{\sqrt{x} }[/tex]
Remember that [tex]\sqrt{x}[/tex] can be written as [tex]x^{\frac{1}{2} }[/tex]
=> [tex]\frac{1}{x^{\frac{1}{2} } }[/tex]
=> [tex]x^{-\frac{1}{2} }[/tex]
(ii) Multiply the coefficient of [tex]x^{-\frac{1}{2} }[/tex] by the power of [tex]x^{-\frac{1}{2} }[/tex]
Coefficient of [tex]x^{-\frac{1}{2} }[/tex] = 1
Power of [tex]x^{-\frac{1}{2} }[/tex] = [tex]-\frac{1}{2}[/tex]
=> ([tex]-\frac{1}{2}[/tex] x 1)[tex]x^{-\frac{1}{2} }[/tex]
=> ([tex]-\frac{1}{2}[/tex] )[tex]x^{-\frac{1}{2} }[/tex]
=> [tex]-\frac{1}{2}[/tex] [tex]x^{-\frac{1}{2} }[/tex]
(iii) Subtract 1 from the power of [tex]x^{-\frac{1}{2} }[/tex]
=> [tex]-\frac{1}{2}[/tex] [tex]x^{(-\frac{1}{2} - 1 )}[/tex]
=> [tex]-\frac{1}{2}[/tex] [tex]x^{-\frac{3}{2}}[/tex]
Therefore, the derivative of 1/root x is [tex]-\frac{1}{2}[/tex] [tex]x^{-\frac{3}{2}}[/tex]
