What is the derivative of f(x)= 1/9 x^3+1/21 x-19 ?

The derivative of f(x)= 1/9 x^3+1/21 x-19 is (x^2)/3+1/21

What is the first derivative of f(x)= 1/9 x^3+1/21 x-19 ?

The first derivative of f(x)= 1/9 x^3+1/21 x-19 is (x^2)/3+1/21

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derivative

\frac{x ^{2}}{3} + \frac{1}{21}

Solution steps

\frac{d}{d x} (\frac{1}{9} x^{3} + \frac{1}{21} x - 19)

Simplify

\frac{1}{9} x^{3} + \frac{1}{21} x - 19 : \frac{x ^{3}}{9} + \frac{x}{21} - 19

= \frac{d}{d x} (\frac{x ^{3}}{9} + \frac{x}{21} - 19)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{x ^{3}}{9}) + \frac{d}{d x} (\frac{x}{21}) - \frac{d}{d x} (19)

\frac{d}{d x} (\frac{x ^{3}}{9}) = \frac{x ^{2}}{3}

\frac{d}{d x} (\frac{x}{21}) = \frac{1}{21}

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

= \frac{x ^{2}}{3} + \frac{1}{21} - 0

Simplify

= \frac{x ^{2}}{3} + \frac{1}{21}

What is the derivative of f(x)= 1/9 x^3+1/21 x-19 ?
The derivative of f(x)= 1/9 x^3+1/21 x-19 is (x^2)/3+1/21
What is the first derivative of f(x)= 1/9 x^3+1/21 x-19 ?
The first derivative of f(x)= 1/9 x^3+1/21 x-19 is (x^2)/3+1/21