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Popular >

derivative of (x^3-3x^2+1^{-3})

Solution

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

Solution

- \frac{3 ( 3 x ^{2} - 6 x )}{( x ^{3} - 3 x ^{2} + 1 ) ^{4}}

Solution steps

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

Apply the chain rule:

- \frac{3}{( x ^{3} - 3 x ^{2} + 1 ) ^{4}} \frac{d}{d x} (x^{3} - 3 x^{2} + 1)

= - \frac{3}{( x ^{3} - 3 x ^{2} + 1 ) ^{4}} \frac{d}{d x} (x^{3} - 3 x^{2} + 1)

\frac{d}{d x} (x^{3} - 3 x^{2} + 1) = 3 x^{2} - 6 x

= - \frac{3}{( x ^{3} - 3 x ^{2} + 1 ) ^{4}} (3 x^{2} - 6 x)

Multiply fractions:

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

= - \frac{3 ( 3 x ^{2} - 6 x )}{( x ^{3} - 3 x ^{2} + 1 ) ^{4}}

Popular Examples

tangent of x^3-9x^2+10x,\at =-2 tangent of

x^{3} - 9 x^{2} + 10 x, at = - 2

sum from n=0 to infinity of (x^n)/(n3^n)

n = 0 \sum \infty \frac{x ^{n}}{n 3 ^{n}}

derivative of (e^x/(2-tan(x)))

\frac{d}{d x} (\frac{e ^{x}}{2 - tan ( x )})

(\partial)/(\partial x)(sin(3x)cos(3y))

\frac{\partial}{\partial x} (sin (3 x) cos (3 y))

tangent of f(x)=5x-3x^2,\at x=1 tangent of

f (x) = 5 x - 3 x^{2}, at x = 1

Frequently Asked Questions (FAQ)

What is the derivative of (x^3-3x^2+1^{-3}) ?
The derivative of (x^3-3x^2+1^{-3}) is -(3(3x^2-6x))/((x^3-3x^2+1)^4)
What is the first derivative of (x^3-3x^2+1^{-3}) ?
The first derivative of (x^3-3x^2+1^{-3}) is -(3(3x^2-6x))/((x^3-3x^2+1)^4)