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

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

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

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

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derivative of

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

x^{2} + x + 1

Solution steps

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

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

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

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

= x^{2} + x + 1

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