What is the derivative of 2/(2-x) ?

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

What is the first derivative of 2/(2-x) ?

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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