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Popular >

derivative of y=|x^2-8|

Solution

derivative of

y = x^{2} - 8

Solution

\frac{2 x ( x ^{2} - 8 )}{∣ x ^{2} - 8 ∣}

Solution steps

\frac{d}{d x} (x^{2} - 8)

Apply the chain rule:

\frac{x ^{2} - 8}{∣ ( x ^{2} - 8 ) ∣} \frac{d}{d x} (x^{2} - 8)

= \frac{x ^{2} - 8}{∣ ( x ^{2} - 8 ) ∣} \frac{d}{d x} (x^{2} - 8)

\frac{d}{d x} (x^{2} - 8) = 2 x

= \frac{x ^{2} - 8}{∣ ( x ^{2} - 8 ) ∣} \cdot 2 x

Multiply fractions:

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

= \frac{2 x ( x ^{2} - 8 )}{∣ x ^{2} - 8 ∣}

Popular Examples

y^{''}-3y^'+2y=4x^2

y^{^{''}} - 3 y^{^{'}} + 2 y = 4 x^{2}

integral of x/(2sqrt(x))

\int \frac{x}{2 x} d x

limit as x approaches infinity of x/k

x \to \infty lim (\frac{x}{k})

derivative of 6x^2-x

\frac{d}{d x} (6 x^{2} - x)

(\partial)/(\partial y)(xsin(yz))

\frac{\partial}{\partial y} (x sin (yz))

Frequently Asked Questions (FAQ)

What is the derivative of y=|x^2-8| ?
The derivative of y=|x^2-8| is (2x(x^2-8))/(|x^2-8|)
What is the first derivative of y=|x^2-8| ?
The first derivative of y=|x^2-8| is (2x(x^2-8))/(|x^2-8|)