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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int x^{2} - 6 x - 7 d x

\int x^{2} \cdot 2^{- x} d x

\int x e^{- 2} d x

f (x) = 4 + 8 x - 5 x^{2}

e^{e^{x^{2}}}

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