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Popular >

derivative of ln|x^2-4|

Solution

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

Solution

\frac{2 x}{x ^{2} - 4}

Solution steps

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

Apply the chain rule:

\frac{1}{∣ x ^{2} - 4 ∣} \frac{d}{d x} (x^{2} - 4)

= \frac{1}{∣ x ^{2} - 4 ∣} \frac{d}{d x} (x^{2} - 4)

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

= \frac{1}{∣ x ^{2} - 4 ∣} \cdot \frac{2 x ( x ^{2} - 4 )}{∣ x ^{2} - 4 ∣}

Simplify

\frac{1}{∣ x ^{2} - 4 ∣} \cdot \frac{2 x ( x ^{2} - 4 )}{∣ x ^{2} - 4 ∣} : \frac{2 x}{x ^{2} - 4}

= \frac{2 x}{x ^{2} - 4}

Popular Examples

derivative of f(x)=-2x^2-12x-4 derivative of

f (x) = - 2 x^{2} - 12 x - 4

(tdy)/(dt)=t^3+8t^3y

\frac{t d y}{d t} = t^{3} + 8 t^{3} y

derivative of ((x+3^2)/(e^x*cos(x)))

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

derivative of f(x)= 1/5 (9x+8)^3 derivative of

f (x) = \frac{1}{5} (9 x + 8)^{3}

derivative of-7ln(x)

\frac{d}{d x} (- 7 ln (x))

Frequently Asked Questions (FAQ)

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