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Popular >

derivative of |x^2-4|

Solution

\frac{d}{d 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 sin(xsin(y)sin(x+y))

\frac{d}{d x} (sin (x) sin (y) sin (x + y))

limit as x approaches 2 of x^3f(x)

x \to 2 lim (x^{3} f (x))

sum from n=1 to infinity of ((-1)^n)/(5(2^{n+2))}

n = 1 \sum \infty \frac{( - 1 ) ^{n}}{5 ( 2 ^{n + 2} )}

limit as x approaches 1+of 7/(1-x)

x \to 1 + lim (\frac{7}{1 - x})

derivative of y=4-3x derivative of

y = 4 - 3 x

Frequently Asked Questions (FAQ)

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