What is the derivative of 1/((x^2-2x-5)^4) ?

The derivative of 1/((x^2-2x-5)^4) is -(4(2x-2))/((x^2-2x-5)^5)

What is the first derivative of 1/((x^2-2x-5)^4) ?

The first derivative of 1/((x^2-2x-5)^4) is -(4(2x-2))/((x^2-2x-5)^5)

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derivative of

\frac{1}{( x ^{2} - 2 x - 5 ) ^{4}}

- \frac{4 ( 2 x - 2 )}{( x ^{2} - 2 x - 5 ) ^{5}}

Solution steps

\frac{d}{d x} (\frac{1}{( x ^{2} - 2 x - 5 ) ^{4}})

Apply exponent rule:

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

= \frac{d}{d x} ((x^{2} - 2 x - 5)^{- 4})

Apply the chain rule:

- \frac{4}{( x ^{2} - 2 x - 5 ) ^{5}} \frac{d}{d x} (x^{2} - 2 x - 5)

= - \frac{4}{( x ^{2} - 2 x - 5 ) ^{5}} \frac{d}{d x} (x^{2} - 2 x - 5)

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

= - \frac{4}{( x ^{2} - 2 x - 5 ) ^{5}} (2 x - 2)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= - \frac{4 ( 2 x - 2 )}{( x ^{2} - 2 x - 5 ) ^{5}}

\int_{0}^{2} \frac{1}{2} y^{2} d y

sin (\frac{t}{t + 9})

\int \frac{2 x + 1}{3 x ^{2} - 27} d x

\int \frac{1}{e ^{- x} + 1} d x

\int \frac{1}{2 + 7 y ^{2}} d y

What is the derivative of 1/((x^2-2x-5)^4) ?
The derivative of 1/((x^2-2x-5)^4) is -(4(2x-2))/((x^2-2x-5)^5)
What is the first derivative of 1/((x^2-2x-5)^4) ?
The first derivative of 1/((x^2-2x-5)^4) is -(4(2x-2))/((x^2-2x-5)^5)