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Popular >

derivative of (x^2-x+1^{-7})

Solution

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

Solution

- \frac{7 ( 2 x - 1 )}{( x ^{2} - x + 1 ) ^{8}}

Solution steps

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

Apply the chain rule:

- \frac{7}{( x ^{2} - x + 1 ) ^{8}} \frac{d}{d x} (x^{2} - x + 1)

= - \frac{7}{( x ^{2} - x + 1 ) ^{8}} \frac{d}{d x} (x^{2} - x + 1)

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

= - \frac{7}{( x ^{2} - x + 1 ) ^{8}} (2 x - 1)

Multiply fractions:

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

= - \frac{7 ( 2 x - 1 )}{( x ^{2} - x + 1 ) ^{8}}

Popular Examples

integral of (x-1)/(x(x^2-5x+6))

\int \frac{x - 1}{x ( x ^{2} - 5 x + 6 )} d x

integral of (3-5x)^2

\int (3 - 5 x)^{2} d x

(dy)/(dx)=2ycos(x)

\frac{d y}{d x} = 2 y cos (x)

limit as x approaches 4 of-x^2-9x-8

x \to 4 lim (- x^{2} - 9 x - 8)

derivative of (5sqrt(x)/(2x^{-2)})

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

Frequently Asked Questions (FAQ)

What is the derivative of (x^2-x+1^{-7}) ?
The derivative of (x^2-x+1^{-7}) is -(7(2x-1))/((x^2-x+1)^8)
What is the first derivative of (x^2-x+1^{-7}) ?
The first derivative of (x^2-x+1^{-7}) is -(7(2x-1))/((x^2-x+1)^8)