What is the derivative of-6/(1-6x) ?

The derivative of-6/(1-6x) is -(36)/((1-6x)^2)

What is the first derivative of-6/(1-6x) ?

The first derivative of-6/(1-6x) is -(36)/((1-6x)^2)

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\frac{d}{d x} (- \frac{6}{1 - 6 x})

- \frac{36}{( 1 - 6 x ) ^{2}}

Solution steps

\frac{d}{d x} (- \frac{6}{1 - 6 x})

Take the constant out:

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

= - 6 \frac{d}{d x} (\frac{1}{1 - 6 x})

Apply exponent rule:

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

= - 6 \frac{d}{d x} ((1 - 6 x)^{- 1})

Apply the chain rule:

- \frac{1}{( 1 - 6 x ) ^{2}} \frac{d}{d x} (1 - 6 x)

= - \frac{1}{( 1 - 6 x ) ^{2}} \frac{d}{d x} (1 - 6 x)

\frac{d}{d x} (1 - 6 x) = - 6

= - 6 (- \frac{1}{( 1 - 6 x ) ^{2}} (- 6))

Simplify

- 6 (- \frac{1}{( 1 - 6 x ) ^{2}} (- 6)) : - \frac{36}{( 1 - 6 x ) ^{2}}

= - \frac{36}{( 1 - 6 x ) ^{2}}

What is the derivative of-6/(1-6x) ?
The derivative of-6/(1-6x) is -(36)/((1-6x)^2)
What is the first derivative of-6/(1-6x) ?
The first derivative of-6/(1-6x) is -(36)/((1-6x)^2)