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

The derivative of (-1)/((x-2)^2) is 2/((x-2)^3)

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

The first derivative of (-1)/((x-2)^2) is 2/((x-2)^3)

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derivative of

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

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

Solution steps

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

Simplify

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

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

Take the constant out:

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

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

Apply exponent rule:

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

= - \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

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

Simplify

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

5 (t) i + (40 - 5 (t)^{2}) j

2 + cos (x)

5^{x} (x^{2} + 1)

\frac{d}{d x} (4 x^{2} + 2 x + 1 n (x) - 3 x^{2} - 7 x - 3)

y = 4 x^{3} (2 - 3 x)

What is the derivative of (-1)/((x-2)^2) ?
The derivative of (-1)/((x-2)^2) is 2/((x-2)^3)
What is the first derivative of (-1)/((x-2)^2) ?
The first derivative of (-1)/((x-2)^2) is 2/((x-2)^3)