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

The derivative of-2/((x-2^2)) is 4/((x-2)^3)

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

The first derivative of-2/((x-2^2)) is 4/((x-2)^3)

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

\frac{4}{( x - 2 ) ^{3}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

- \frac{2}{( x - 2 ) ^{3}} \frac{d}{d x} (x - 2)

= - \frac{2}{( x - 2 ) ^{3}} \frac{d}{d x} (x - 2)

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

= - 2 (- \frac{2}{( x - 2 ) ^{3}} \cdot 1)

Simplify

- 2 (- \frac{2}{( x - 2 ) ^{3}} \cdot 1) : \frac{4}{( x - 2 ) ^{3}}

= \frac{4}{( x - 2 ) ^{3}}

x \to 2 lim ((\frac{x + 3}{2 x + 1})^{\frac{2}{x - 2}})

\frac{d}{d x} (x arccos (3 x))

\int_{- 2}^{4} \frac{1}{( x - 3 ) ^{3}} d x

\frac{d y}{d x}, y = 2 x^{3}

\int e^{3 x} sin (4 x) d x

What is the derivative of-2/((x-2^2)) ?
The derivative of-2/((x-2^2)) is 4/((x-2)^3)
What is the first derivative of-2/((x-2^2)) ?
The first derivative of-2/((x-2^2)) is 4/((x-2)^3)