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}} (- 3))

Simplify

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

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

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)