What is the derivative of (2x^3)/3+(x^2)/2+6x+6 ?

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

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

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

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derivative of

\frac{2 x ^{3}}{3} + \frac{x ^{2}}{2} + 6 x + 6

2 x^{2} + x + 6

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

\frac{d}{d x} (6) = 0

= 2 x^{2} + x + 6 + 0

Simplify

= 2 x^{2} + x + 6

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