What is the derivative of 1/3 x^3-x^2+x+100 ?

The derivative of 1/3 x^3-x^2+x+100 is x^2-2x+1

What is the first derivative of 1/3 x^3-x^2+x+100 ?

The first derivative of 1/3 x^3-x^2+x+100 is x^2-2x+1

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\frac{d}{d x} (\frac{1}{3} x^{3} - x^{2} + x + 100)

x^{2} - 2 x + 1

Solution steps

\frac{d}{d x} (\frac{1}{3} x^{3} - x^{2} + x + 100)

Simplify

\frac{1}{3} x^{3} - x^{2} + x + 100 : \frac{x ^{3}}{3} - x^{2} + x + 100

= \frac{d}{d x} (\frac{x ^{3}}{3} - x^{2} + x + 100)

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 x}{d x} + \frac{d}{d x} (100)

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

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

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

\frac{d}{d x} (100) = 0

= x^{2} - 2 x + 1 + 0

Simplify

= x^{2} - 2 x + 1

What is the derivative of 1/3 x^3-x^2+x+100 ?
The derivative of 1/3 x^3-x^2+x+100 is x^2-2x+1
What is the first derivative of 1/3 x^3-x^2+x+100 ?
The first derivative of 1/3 x^3-x^2+x+100 is x^2-2x+1