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Popular >

derivative of ln(x+sqrt(x^2-4))

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

y^{''}-9y^'+18y=0

y^{^{''}} - 9 y^{^{'}} + 18 y = 0

derivative of x/(y^{13)}+Be^y derivative of

\frac{x}{y ^{13}} + B e^{y}

integral of (csc^4(θ))

\int (csc^{4} (θ)) d θ

derivative of (2x^3-4x^2(3x^5+x^2))

\frac{d}{d x} ((2 x^{3} - 4 x^{2}) (3 x^{5} + x^{2}))

integral of 2/(x^2+3x-4)

\int \frac{2}{x ^{2} + 3 x - 4} d x

Frequently Asked Questions (FAQ)

What is the derivative of ln(x+sqrt(x^2-4)) ?
The derivative of ln(x+sqrt(x^2-4)) is 1/(sqrt(x^2-4))
What is the first derivative of ln(x+sqrt(x^2-4)) ?
The first derivative of ln(x+sqrt(x^2-4)) is 1/(sqrt(x^2-4))