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

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

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

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

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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