What is the derivative of 4/(x-2) ?

The derivative of 4/(x-2) is -4/((x-2)^2)

What is the first derivative of 4/(x-2) ?

The first derivative of 4/(x-2) is -4/((x-2)^2)

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\frac{d}{d x} (\frac{4}{x - 2})

- \frac{4}{( x - 2 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{4}{x - 2})

Take the constant out:

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

= 4 \frac{d}{d x} (\frac{1}{x - 2})

Apply exponent rule:

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

= 4 \frac{d}{d x} ((x - 2)^{- 1})

Apply the chain rule:

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

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

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

= 4 (- \frac{1}{( x - 2 ) ^{2}} \cdot 1)

Simplify

4 (- \frac{1}{( x - 2 ) ^{2}} \cdot 1) : - \frac{4}{( x - 2 ) ^{2}}

= - \frac{4}{( x - 2 ) ^{2}}

\frac{d}{d x} (ln (3 + 2 x))

x \to 1 lim (x^{2} + 1)

\int 1 + x d x

(3 x + 5)^{4} x

\int t e^{- 2} d t

What is the derivative of 4/(x-2) ?
The derivative of 4/(x-2) is -4/((x-2)^2)
What is the first derivative of 4/(x-2) ?
The first derivative of 4/(x-2) is -4/((x-2)^2)