What is the derivative of 5/(1-9x) ?

The derivative of 5/(1-9x) is (45)/((1-9x)^2)

What is the first derivative of 5/(1-9x) ?

The first derivative of 5/(1-9x) is (45)/((1-9x)^2)

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\frac{d}{d x} (\frac{5}{1 - 9 x})

\frac{45}{( 1 - 9 x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{5}{1 - 9 x})

Take the constant out:

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

= 5 \frac{d}{d x} (\frac{1}{1 - 9 x})

Apply exponent rule:

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

= 5 \frac{d}{d x} ((1 - 9 x)^{- 1})

Apply the chain rule:

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

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

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

= 5 (- \frac{1}{( 1 - 9 x ) ^{2}} (- 9))

Simplify

5 (- \frac{1}{( 1 - 9 x ) ^{2}} (- 9)) : \frac{45}{( 1 - 9 x ) ^{2}}

= \frac{45}{( 1 - 9 x ) ^{2}}

What is the derivative of 5/(1-9x) ?
The derivative of 5/(1-9x) is (45)/((1-9x)^2)
What is the first derivative of 5/(1-9x) ?
The first derivative of 5/(1-9x) is (45)/((1-9x)^2)