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Popular >

derivative of f(x)=|x^2-4|

Solution

derivative of

f (x) = x^{2} - 4

Solution

\frac{2 x ( x ^{2} - 4 )}{∣ x ^{2} - 4 ∣}

Solution steps

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

Apply the chain rule:

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

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

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

= \frac{x ^{2} - 4}{∣ ( x ^{2} - 4 ) ∣} \cdot 2 x

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 x ( x ^{2} - 4 )}{∣ x ^{2} - 4 ∣}

Popular Examples

derivative of 1/(2-cos(pix))

\frac{d}{d x} (\frac{1}{2 - cos ( π ) x})

limit as x approaches-6+of 1/((x+6)^4)

x \to - 6 + lim (\frac{1}{( x + 6 ) ^{4}})

- 2 y^{2} d y = y^{3} v d v

limit as x approaches 4 of (5x+7)^4

x \to 4 lim ((5 x + 7)^{4})

integral of (4x^3+2x^2+8)/((x^2+4)^2)

\int \frac{4 x ^{3} + 2 x ^{2} + 8}{( x ^{2} + 4 ) ^{2}} d x

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=|x^2-4| ?
The derivative of f(x)=|x^2-4| is (2x(x^2-4))/(|x^2-4|)
What is the first derivative of f(x)=|x^2-4| ?
The first derivative of f(x)=|x^2-4| is (2x(x^2-4))/(|x^2-4|)