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Popular >

derivative of (x^9-3x)^{-2}

Solution

derivative of

(x^{9} - 3 x)^{- 2}

Solution

- \frac{2 ( 9 x ^{8} - 3 )}{( x ^{9} - 3 x ) ^{3}}

Solution steps

\frac{d}{d x} ((x^{9} - 3 x)^{- 2})

Apply the chain rule:

- \frac{2}{( x ^{9} - 3 x ) ^{3}} \frac{d}{d x} (x^{9} - 3 x)

= - \frac{2}{( x ^{9} - 3 x ) ^{3}} \frac{d}{d x} (x^{9} - 3 x)

\frac{d}{d x} (x^{9} - 3 x) = 9 x^{8} - 3

= - \frac{2}{( x ^{9} - 3 x ) ^{3}} (9 x^{8} - 3)

Multiply fractions:

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

= - \frac{2 ( 9 x ^{8} - 3 )}{( x ^{9} - 3 x ) ^{3}}

Popular Examples

integral of (y+1)

\int (y + 1) d y

(dy)/(dx)-(xy)/(1+x)=x

\frac{d y}{d x} - \frac{x y}{1 + x} = x

(\partial)/(\partial x)(ln(4x^2+9y^2+8))

\frac{\partial}{\partial x} (ln (4 x^{2} + 9 y^{2} + 8))

y^{^{''}} + 2 y = 1

y^{''}+2y=sin(xsqrt(2))

y^{^{''}} + 2 y = sin (x 2)

Frequently Asked Questions (FAQ)

What is the derivative of (x^9-3x)^{-2} ?
The derivative of (x^9-3x)^{-2} is -(2(9x^8-3))/((x^9-3x)^3)
What is the first derivative of (x^9-3x)^{-2} ?
The first derivative of (x^9-3x)^{-2} is -(2(9x^8-3))/((x^9-3x)^3)