What is the derivative of 1/3 x^3-1/2 x^2-6x ?

The derivative of 1/3 x^3-1/2 x^2-6x is x^2-x-6

What is the first derivative of 1/3 x^3-1/2 x^2-6x ?

The first derivative of 1/3 x^3-1/2 x^2-6x is x^2-x-6

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

x^{2} - x - 6

Solution steps

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

Simplify

\frac{1}{3} x^{3} - \frac{1}{2} x^{2} - 6 x : \frac{x ^{3}}{3} - \frac{x ^{2}}{2} - 6 x

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

Apply the Sum/Difference Rule:

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

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

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

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

\frac{d}{d x} (6 x) = 6

= x^{2} - x - 6

What is the derivative of 1/3 x^3-1/2 x^2-6x ?
The derivative of 1/3 x^3-1/2 x^2-6x is x^2-x-6
What is the first derivative of 1/3 x^3-1/2 x^2-6x ?
The first derivative of 1/3 x^3-1/2 x^2-6x is x^2-x-6