What is (\partial)/(\partial x)(1/(sqrt(x+2))) ?

The answer to (\partial)/(\partial x)(1/(sqrt(x+2))) is -1/(2(x+2)^{3/2)}

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(\partial)/(\partial x)(1/(sqrt(x+2)))

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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What is (\partial)/(\partial x)(1/(sqrt(x+2))) ?
The answer to (\partial)/(\partial x)(1/(sqrt(x+2))) is -1/(2(x+2)^{3/2)}