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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

= 2 \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

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

Simplify

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

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

\frac{d}{d x} (5 e^{- x} + e^{4 x})

x^{3} y^{^{'''}} - x^{2} y^{^{''}} + 2 x y^{^{'}} - 2 y = x

\int_{0}^{1} π (x^{2} - x^{6}) d x

t \to 0 lim (\frac{tan ^{2} ( 3 t )}{2 t})

\int e^{\frac{x}{7}} d x

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