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Popular >

derivative of y=x|x|

Solution

derivative of

y = 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 e^x(x^2+3(x^3+4))

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

y^{^{''}} + y^{^{'}} = 0

integral of 1/(1+144x^2)

\int \frac{1}{1 + 144 x ^{2}} d x

integral of (sin(ln(4)x^2))/x

\int \frac{sin ( ln ( 4 ) x ^{2} )}{x} d x

inverse oflaplace (-4e^{(-2s)})/((s^2-6s+8))inverse laplace

\frac{- 4 e ^{(- 2 s)}}{( s ^{2} - 6 s + 8 )}

Frequently Asked Questions (FAQ)

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