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

The derivative of 1/(x+9) is -1/((x+9)^2)

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

The first derivative of 1/(x+9) is -1/((x+9)^2)

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derivative of

\frac{1}{x + 9}

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

Apply the chain rule:

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

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

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

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

Simplify

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

\int \frac{e ^{\frac{x}{2}}}{x} d x

\int 7 x^{3} + 4 x^{2} d x

\frac{3}{2 x}

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

x

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