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

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

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

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

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derivative

x^{2}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Sum/Difference Rule:

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

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

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

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

= \frac{1}{3} (3 x^{2} + 0)

Simplify

\frac{1}{3} (3 x^{2} + 0) : x^{2}

= x^{2}

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