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

The derivative of ln(x^2+x) is (2x+1)/(x^2+x)

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

The first derivative of ln(x^2+x) is (2x+1)/(x^2+x)

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derivative of

ln (x^{2} + x)

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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