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

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

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

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

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

x - 1 + \frac{x ^{2}}{2}

Solution steps

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

Simplify

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

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d x}{d x} = 1

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

= x - 1 + \frac{x ^{2}}{2}

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