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Popular >

derivative of 1/(sqrt(2+x))

Solution

\frac{d}{d x} (\frac{1}{2 + x})

Solution

- \frac{1}{2 ( 2 + x ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{1}{2 + x})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= \frac{d}{d x} ((2 + x)^{- \frac{1}{2}})

Apply the chain rule:

- \frac{1}{2 ( 2 + x ) ^{\frac{3}{2}}} \frac{d}{d x} (2 + x)

= - \frac{1}{2 ( 2 + x ) ^{\frac{3}{2}}} \frac{d}{d x} (2 + x)

\frac{d}{d x} (2 + x) = 1

= - \frac{1}{2 ( 2 + x ) ^{\frac{3}{2}}} \cdot 1

Simplify

= - \frac{1}{2 ( 2 + x ) ^{\frac{3}{2}}}

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Frequently Asked Questions (FAQ)

What is the derivative of 1/(sqrt(2+x)) ?
The derivative of 1/(sqrt(2+x)) is -1/(2(2+x)^{3/2)}
What is the first derivative of 1/(sqrt(2+x)) ?
The first derivative of 1/(sqrt(2+x)) is -1/(2(2+x)^{3/2)}