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

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

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

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

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

x^{2} + x

Solution steps

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

Simplify

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

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

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} (2)

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

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

\frac{d}{d x} (2) = 0

= x^{2} + x + 0

Simplify

= x^{2} + x

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