What is the derivative of 1/3 x^3-x^2-8x+1 ?

The derivative of 1/3 x^3-x^2-8x+1 is x^2-2x-8

What is the first derivative of 1/3 x^3-x^2-8x+1 ?

The first derivative of 1/3 x^3-x^2-8x+1 is x^2-2x-8

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\frac{d}{d x} (\frac{1}{3} x^{3} - x^{2} - 8 x + 1)

x^{2} - 2 x - 8

Solution steps

\frac{d}{d x} (\frac{1}{3} x^{3} - x^{2} - 8 x + 1)

Simplify

\frac{1}{3} x^{3} - x^{2} - 8 x + 1 : \frac{x ^{3}}{3} - x^{2} - 8 x + 1

= \frac{d}{d x} (\frac{x ^{3}}{3} - x^{2} - 8 x + 1)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{x ^{3}}{3}) - \frac{d}{d x} (x^{2}) - \frac{d}{d x} (8 x) + \frac{d}{d x} (1)

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

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

\frac{d}{d x} (8 x) = 8

\frac{d}{d x} (1) = 0

= x^{2} - 2 x - 8 + 0

Simplify

= x^{2} - 2 x - 8

y^{^{'}} = \frac{2 x ^{4} + y ^{4}}{x y ^{3}}

2 x \frac{d y}{d x} = y^{2}

y^{^{'}} = 9 x + y - 9

\int \frac{x}{x - 6} d x

\frac{\partial}{\partial x} (2 y - sin (x))

What is the derivative of 1/3 x^3-x^2-8x+1 ?
The derivative of 1/3 x^3-x^2-8x+1 is x^2-2x-8
What is the first derivative of 1/3 x^3-x^2-8x+1 ?
The first derivative of 1/3 x^3-x^2-8x+1 is x^2-2x-8