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Popular >

derivative of y=ln(sqrt(x^2-4))

Solution

derivative of

y = ln (x^{2} - 4)

Solution

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

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

Simplify

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

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

Popular Examples

limit as x approaches 2 of 3-x^{1/(x^2)}

x \to 2 lim (3 - x^{\frac{1}{x ^{2}}})

derivative of (sqrt(x)dx)

\frac{d}{d x} ((x) d x)

derivative of cos((1-e^{6x}/(1+e^{6x)}))

\frac{d}{d x} (cos (\frac{1 - e ^{6 x}}{1 + e ^{6 x}}))

limit as x approaches infinity of 9.9

x \to \infty lim (9.9)

y^'=(x-y)/(x+y)

y^{^{'}} = \frac{x - y}{x + y}

Frequently Asked Questions (FAQ)

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