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Popular >

derivative of |x^2-1|

Solution

\frac{d}{d x} (x^{2} - 1)

Solution

\frac{2 x ( x ^{2} - 1 )}{∣ x ^{2} - 1 ∣}

Solution steps

\frac{d}{d x} (x^{2} - 1)

Apply the chain rule:

\frac{x ^{2} - 1}{∣ ( x ^{2} - 1 ) ∣} \frac{d}{d x} (x^{2} - 1)

= \frac{x ^{2} - 1}{∣ ( x ^{2} - 1 ) ∣} \frac{d}{d x} (x^{2} - 1)

\frac{d}{d x} (x^{2} - 1) = 2 x

= \frac{x ^{2} - 1}{∣ ( x ^{2} - 1 ) ∣} \cdot 2 x

Multiply fractions:

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

= \frac{2 x ( x ^{2} - 1 )}{∣ x ^{2} - 1 ∣}

Popular Examples

integral from 0 to 1 of (23)/(4x-1)

\int_{0}^{1} \frac{23}{4 x - 1} d x

implicit (dy)/(dx),y^5=x^3 implicit derivative

\frac{d y}{d x}, y^{5} = x^{3}

integral of 5sec^2(1+5x)

\int 5 sec^{2} (1 + 5 x) d x

1/(x^8)(dy)/(dx)=12+15y

\frac{1}{x ^{8}} \frac{d y}{d x} = 12 + 15 y

derivative of 5/(ln(x))derivative of

\frac{5}{ln ( x )}

Frequently Asked Questions (FAQ)

What is the derivative of |x^2-1| ?
The derivative of |x^2-1| is (2x(x^2-1))/(|x^2-1|)
What is the first derivative of |x^2-1| ?
The first derivative of |x^2-1| is (2x(x^2-1))/(|x^2-1|)