What is the derivative of 1/(sqrt(x+9)) ?

The derivative of 1/(sqrt(x+9)) is -1/(2(x+9)^{3/2)}

What is the first derivative of 1/(sqrt(x+9)) ?

The first derivative of 1/(sqrt(x+9)) is -1/(2(x+9)^{3/2)}

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derivative of

\frac{1}{x + 9}

- \frac{1}{2 ( x + 9 ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{1}{x + 9})

Apply exponent rule:

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

= \frac{d}{d x} ((x + 9)^{- \frac{1}{2}})

Apply the chain rule:

- \frac{1}{2 ( x + 9 ) ^{\frac{3}{2}}} \frac{d}{d x} (x + 9)

= - \frac{1}{2 ( x + 9 ) ^{\frac{3}{2}}} \frac{d}{d x} (x + 9)

\frac{d}{d x} (x + 9) = 1

= - \frac{1}{2 ( x + 9 ) ^{\frac{3}{2}}} \cdot 1

Simplify

= - \frac{1}{2 ( x + 9 ) ^{\frac{3}{2}}}

\frac{d}{d x} (arccos (arcsin (t)))

\frac{d}{d s} (\frac{3 s ^{3} + 19 s ^{2} + 41 s + 26}{( s + 1 )})

\frac{\partial}{\partial x} (x sin (\frac{8}{x}))

x \to 0 lim (cos^{2} (x) \cdot x)

n = 0 \sum \infty \frac{1}{n + 16}

What is the derivative of 1/(sqrt(x+9)) ?
The derivative of 1/(sqrt(x+9)) is -1/(2(x+9)^{3/2)}
What is the first derivative of 1/(sqrt(x+9)) ?
The first derivative of 1/(sqrt(x+9)) is -1/(2(x+9)^{3/2)}