What is the derivative of 1/(sqrt(x+5)) ?

The derivative of 1/(sqrt(x+5)) is -1/(2(x+5)^{3/2)}

What is the first derivative of 1/(sqrt(x+5)) ?

The first derivative of 1/(sqrt(x+5)) is -1/(2(x+5)^{3/2)}

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\frac{d}{d x} (\frac{1}{x + 5})

- \frac{1}{2 ( x + 5 ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{1}{x + 5})

Apply exponent rule:

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

= \frac{d}{d x} ((x + 5)^{- \frac{1}{2}})

Apply the chain rule:

- \frac{1}{2 ( x + 5 ) ^{\frac{3}{2}}} \frac{d}{d x} (x + 5)

= - \frac{1}{2 ( x + 5 ) ^{\frac{3}{2}}} \frac{d}{d x} (x + 5)

\frac{d}{d x} (x + 5) = 1

= - \frac{1}{2 ( x + 5 ) ^{\frac{3}{2}}} \cdot 1

Simplify

= - \frac{1}{2 ( x + 5 ) ^{\frac{3}{2}}}

What is the derivative of 1/(sqrt(x+5)) ?
The derivative of 1/(sqrt(x+5)) is -1/(2(x+5)^{3/2)}
What is the first derivative of 1/(sqrt(x+5)) ?
The first derivative of 1/(sqrt(x+5)) is -1/(2(x+5)^{3/2)}