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Popular >

derivative of ln(x^2+2x)

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

limit as x approaches 0 of ln(2x^2+x)

x \to 0 lim (ln (2 x^{2} + x))

integral of x/(x^2+49)

\int \frac{x}{x ^{2} + 49} d x

inverse oflaplace 1/((s-3)(s-9))inverse laplace

\frac{1}{( s - 3 ) ( s - 9 )}

limit as (x,y) approaches (0,0) of ((sin(2x)-2x+y))/(x^3+y)

(x, y) \to (0, 0) lim (\frac{( sin ( 2 x ) - 2 x + y )}{x ^{3} + y})

integral of ln(x)*ln(x)

\int ln (x) \cdot ln (x) d x

Frequently Asked Questions (FAQ)

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