What is the derivative of ln(x^2+4x) ?

The derivative of ln(x^2+4x) is (2x+4)/(x^2+4x)

What is the first derivative of ln(x^2+4x) ?

The first derivative of ln(x^2+4x) is (2x+4)/(x^2+4x)

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

y = x, y = 2 - x, y = 0

y = 2 sin (x), y = e^{x}, x = 0, x = \frac{π}{2}

y^{^{'}} = x^{2} - 3 y

\int (e^{- x}) d x

x^{^{'}} = 0

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