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Popular >

derivative of f(x)=x|x|

Solution

derivative of

f (x) = x ∣ x ∣

Solution

\frac{2 x ^{2}}{∣ x ∣}

Solution steps

\frac{d}{d x} (x ∣ x ∣)

Apply the Product Rule:

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

f = x, g = ∣ x ∣

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

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

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

= 1 \cdot ∣ x ∣ + \frac{x}{∣ x ∣} x

Simplify

1 \cdot ∣ x ∣ + \frac{x}{∣ x ∣} x : \frac{2 x ^{2}}{∣ x ∣}

= \frac{2 x ^{2}}{∣ x ∣}

Popular Examples

derivative of f(x)=5x-4 derivative of

f (x) = 5 x - 4

integral from 1/3 to 5 of 12xln(3x)

\int_{\frac{1}{3}}^{5} 12 x ln (3 x) d x

integral of tan^2(xco)s^3x

\int tan^{2} (x co) s^{3} x d x

limit as x approaches-2 of (-3)/(x+2)

x \to - 2 lim (\frac{- 3}{x + 2})

integral of e^{x+3e^x}

\int e^{x + 3 e^{x}} d x

Frequently Asked Questions (FAQ)

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