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Popular >

derivative of ln(x+sqrt(x^2+5))

Solution

\frac{d}{d x} (ln (x + x^{2} + 5))

Solution

\frac{1}{x ^{2} + 5}

Solution steps

\frac{d}{d x} (ln (x + x^{2} + 5))

Apply the chain rule:

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

= \frac{1}{x + x ^{2} + 5} \frac{d}{d x} (x + x^{2} + 5)

\frac{d}{d x} (x + x^{2} + 5) = 1 + \frac{x}{x ^{2} + 5}

= \frac{1}{x + x ^{2} + 5} (1 + \frac{x}{x ^{2} + 5})

Simplify

\frac{1}{x + x ^{2} + 5} (1 + \frac{x}{x ^{2} + 5}) : \frac{1}{x ^{2} + 5}

= \frac{1}{x ^{2} + 5}

Popular Examples

integral from 1 to 3 of 1/(x^2-2x+5)

\int_{1}^{3} \frac{1}{x ^{2} - 2 x + 5} d x

integral of e^{i7x}cos(4x)

\int e^{i 7 x} cos (4 x) d x

integral of e^{2x}x^3

\int e^{2 x} x^{3} d x

inverse oflaplace ((s-1))/(4s^2+s+24)inverse laplace

\frac{( s - 1 )}{4 s ^{2} + s + 24}

derivative of (2x^3-3x^2/((x-1)^2))

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

Frequently Asked Questions (FAQ)

What is the derivative of ln(x+sqrt(x^2+5)) ?
The derivative of ln(x+sqrt(x^2+5)) is 1/(sqrt(x^2+5))
What is the first derivative of ln(x+sqrt(x^2+5)) ?
The first derivative of ln(x+sqrt(x^2+5)) is 1/(sqrt(x^2+5))