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Popular >

derivative of x^2|x|

Solution

\frac{d}{d x} (x^{2} ∣ x ∣)

Solution

\frac{3 x ^{3}}{∣ x ∣}

Solution steps

\frac{d}{d x} (x^{2} ∣ x ∣)

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2}, g = ∣ x ∣

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

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

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

= 2 x ∣ x ∣ + \frac{x}{∣ x ∣} x^{2}

Simplify

2 x ∣ x ∣ + \frac{x}{∣ x ∣} x^{2} : \frac{3 x ^{3}}{∣ x ∣}

= \frac{3 x ^{3}}{∣ x ∣}

Popular Examples

derivative of sqrt((x^2/(cos(x))))

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

derivative of 3x^2-3/(x^4)

\frac{d}{d x} (3 x^{2} - \frac{3}{x ^{4}})

derivative of arctan((x+y^2))

\frac{d}{d x} (arctan ((x + y)^{2}))

limit as x approaches-1-of 5x+2p(x)

x \to - 1 - lim (5 x + 2 p (x))

derivative of f(x)=(5^x)/(cos(x))derivative of

f (x) = \frac{5 ^{x}}{cos ( x )}

Frequently Asked Questions (FAQ)

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