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Popular >

derivative of ln(sqrt(x^2+20))

Solution

\frac{d}{d x} (ln (x^{2} + 20))

Solution

\frac{x}{x ^{2} + 20}

Solution steps

\frac{d}{d x} (ln (x^{2} + 20))

Apply the chain rule:

\frac{1}{x ^{2} + 20} \frac{d}{d x} (x^{2} + 20)

= \frac{1}{x ^{2} + 20} \frac{d}{d x} (x^{2} + 20)

\frac{d}{d x} (x^{2} + 20) = \frac{x}{x ^{2} + 20}

= \frac{1}{x ^{2} + 20} \cdot \frac{x}{x ^{2} + 20}

Simplify

\frac{1}{x ^{2} + 20} \cdot \frac{x}{x ^{2} + 20} : \frac{x}{x ^{2} + 20}

= \frac{x}{x ^{2} + 20}

Popular Examples

(\partial)/(\partial x)((2y)/(x^2+1))

\frac{\partial}{\partial x} (\frac{2 y}{x ^{2} + 1})

limit as x approaches 3 of (x-2)/(x+2)

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

limit as x approaches 1800 of 28pi^2

x \to 1800 lim (28 π^{2})

derivative of (x^2-8x+5)/(x^2+8)derivative of

\frac{x ^{2} - 8 x + 5}{x ^{2} + 8}

integral of 1/(4xsqrt(x^2-16))

\int \frac{1}{4 x x ^{2} - 16} d x

Frequently Asked Questions (FAQ)

What is the derivative of ln(sqrt(x^2+20)) ?
The derivative of ln(sqrt(x^2+20)) is x/(x^2+20)
What is the first derivative of ln(sqrt(x^2+20)) ?
The first derivative of ln(sqrt(x^2+20)) is x/(x^2+20)