What is (\partial)/(\partial x)(ln(x^2+2x)) ?

The answer to (\partial)/(\partial x)(ln(x^2+2x)) is (2x+2)/(x^2+2x)

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(\partial)/(\partial x)(ln(x^2+2x))

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{\partial}{\partial 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}

\frac{\partial}{\partial x} (- 3 y^{3} + 3 x^{2} y^{2} - y)

y^{^{'}} = 24 x^{2} e^{- y}

\int 4 - 3 (1 - x^{2})^{- 1} d x

\frac{d}{d x} y - y = 4

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

What is (\partial)/(\partial x)(ln(x^2+2x)) ?
The answer to (\partial)/(\partial x)(ln(x^2+2x)) is (2x+2)/(x^2+2x)