What is the derivative of 5/((x^2-2x)^2) ?

The derivative of 5/((x^2-2x)^2) is -(10(2x-2))/((x^2-2x)^3)

What is the first derivative of 5/((x^2-2x)^2) ?

The first derivative of 5/((x^2-2x)^2) is -(10(2x-2))/((x^2-2x)^3)

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derivative of

\frac{5}{( x ^{2} - 2 x ) ^{2}}

- \frac{10 ( 2 x - 2 )}{( x ^{2} - 2 x ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{5}{( x ^{2} - 2 x ) ^{2}})

Take the constant out:

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

= 5 \frac{d}{d x} (\frac{1}{( x ^{2} - 2 x ) ^{2}})

Apply exponent rule:

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

= 5 \frac{d}{d x} ((x^{2} - 2 x)^{- 2})

Apply the chain rule:

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

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

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

= 5 (- \frac{2}{( x ^{2} - 2 x ) ^{3}} (2 x - 2))

Simplify

5 (- \frac{2}{( x ^{2} - 2 x ) ^{3}} (2 x - 2)) : - \frac{10 ( 2 x - 2 )}{( x ^{2} - 2 x ) ^{3}}

= - \frac{10 ( 2 x - 2 )}{( x ^{2} - 2 x ) ^{3}}

\frac{d}{d x} (sin (2 cos (3 x)))

\int \frac{x}{( x ^{2} + 25 ) ^{\frac{1}{2}}} d x

\int_{- 5}^{3} \frac{x}{x ^{2} - 9} d x

f (x) = \frac{1 - 2 t}{3 + t}

\frac{d}{d x} (\frac{1}{10} + x e^{- x})

What is the derivative of 5/((x^2-2x)^2) ?
The derivative of 5/((x^2-2x)^2) is -(10(2x-2))/((x^2-2x)^3)
What is the first derivative of 5/((x^2-2x)^2) ?
The first derivative of 5/((x^2-2x)^2) is -(10(2x-2))/((x^2-2x)^3)