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Popular >

derivative of y=(5x^2-6x)^{-2}

Solution

derivative of

y = (5 x^{2} - 6 x)^{- 2}

Solution

- \frac{2 ( 10 x - 6 )}{( 5 x ^{2} - 6 x ) ^{3}}

Solution steps

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

Apply the chain rule:

- \frac{2}{( 5 x ^{2} - 6 x ) ^{3}} \frac{d}{d x} (5 x^{2} - 6 x)

= - \frac{2}{( 5 x ^{2} - 6 x ) ^{3}} \frac{d}{d x} (5 x^{2} - 6 x)

\frac{d}{d x} (5 x^{2} - 6 x) = 10 x - 6

= - \frac{2}{( 5 x ^{2} - 6 x ) ^{3}} (10 x - 6)

Multiply fractions:

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

= - \frac{2 ( 10 x - 6 )}{( 5 x ^{2} - 6 x ) ^{3}}

Popular Examples

integral of (sec(x)tan(x))/(sec(x)-6)

\int \frac{sec ( x ) tan ( x )}{sec ( x ) - 6} d x

integral of x^2e^xsin(x)

\int x^{2} e^{x} sin (x) d x

integral of 1/(x(x-3)^2)

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

(\partial)/(\partial x)(xy+xe^{1/y})

\frac{\partial}{\partial x} (x y + x e^{\frac{1}{y}})

integral of sec^2(u)

\int sec^{2} (u) d u

Frequently Asked Questions (FAQ)

What is the derivative of y=(5x^2-6x)^{-2} ?
The derivative of y=(5x^2-6x)^{-2} is -(2(10x-6))/((5x^2-6x)^3)
What is the first derivative of y=(5x^2-6x)^{-2} ?
The first derivative of y=(5x^2-6x)^{-2} is -(2(10x-6))/((5x^2-6x)^3)