What is the derivative of 3/(1+3x) ?

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

What is the first derivative of 3/(1+3x) ?

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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