What is the derivative of |x|^3-x^2 ?

The derivative of |x|^3-x^2 is (3x^3)/(|x|)-2x

What is the first derivative of |x|^3-x^2 ?

The first derivative of |x|^3-x^2 is (3x^3)/(|x|)-2x

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\frac{d}{d x} (∣ x ∣^{3} - x^{2})

\frac{3 x ^{3}}{∣ x ∣} - 2 x

Solution steps

\frac{d}{d x} (∣ x ∣^{3} - x^{2})

Apply the Sum/Difference Rule:

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

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

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

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

= \frac{3 x ^{3}}{∣ x ∣} - 2 x

x \to \infty lim (\frac{12 x ^{3} - 4 x + 1}{1 + 3 x + 2 x ^{3}})

\frac{8 x - 7}{5 x + 12}

\frac{d}{d x} (f (x) (x)^{- 1} (a x))

\frac{d}{d t} (t^{2} - 1)

\int \frac{sin ( x )}{2 e ^{x}} d x

What is the derivative of |x|^3-x^2 ?
The derivative of |x|^3-x^2 is (3x^3)/(|x|)-2x
What is the first derivative of |x|^3-x^2 ?
The first derivative of |x|^3-x^2 is (3x^3)/(|x|)-2x