What is the derivative of 3/(x+9) ?

The derivative of 3/(x+9) is -3/((x+9)^2)

What is the first derivative of 3/(x+9) ?

The first derivative of 3/(x+9) is -3/((x+9)^2)

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\frac{d}{d x} (\frac{3}{x + 9})

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

Solution steps

\frac{d}{d x} (\frac{3}{x + 9})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply exponent rule:

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

= 3 \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

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

Simplify

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

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

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