What is the derivative of x-1/3 x^3 ?

The derivative of x-1/3 x^3 is 1-x^2

What is the first derivative of x-1/3 x^3 ?

The first derivative of x-1/3 x^3 is 1-x^2

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\frac{d}{d x} (x - \frac{1}{3} x^{3})

1 - x^{2}

Solution steps

\frac{d}{d x} (x - \frac{1}{3} x^{3})

Simplify

x - \frac{1}{3} x^{3} : x - \frac{x ^{3}}{3}

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

Apply the Sum/Difference Rule:

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

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

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

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

= 1 - x^{2}

What is the derivative of x-1/3 x^3 ?
The derivative of x-1/3 x^3 is 1-x^2
What is the first derivative of x-1/3 x^3 ?
The first derivative of x-1/3 x^3 is 1-x^2