What is the derivative of x-x^3 ?

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

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

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

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derivative of

x - x^{3}

1 - 3 x^{2}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

= 1 - 3 x^{2}