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

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

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

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

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derivative of

\frac{5}{1 - x}

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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