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Popular Calculus >

derivative of f(x)=(x^3)/3+4x^2+12x+19

Solution

derivative of

f (x) = \frac{x ^{3}}{3} + 4 x^{2} + 12 x + 19

Solution

x^{2} + 8 x + 12

Solution steps

\frac{d}{d x} (\frac{x ^{3}}{3} + 4 x^{2} + 12 x + 19)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{x ^{3}}{3}) + \frac{d}{d x} (4 x^{2}) + \frac{d}{d x} (12 x) + \frac{d}{d x} (19)

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

\frac{d}{d x} (4 x^{2}) = 8 x

\frac{d}{d x} (12 x) = 12

\frac{d}{d x} (19) = 0

= x^{2} + 8 x + 12 + 0

Simplify

= x^{2} + 8 x + 12

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(x^3)/3+4x^2+12x+19 ?
The derivative of f(x)=(x^3)/3+4x^2+12x+19 is x^2+8x+12
What is the first derivative of f(x)=(x^3)/3+4x^2+12x+19 ?
The first derivative of f(x)=(x^3)/3+4x^2+12x+19 is x^2+8x+12