What is the derivative of ln(x^2+3x+5) ?

The derivative of ln(x^2+3x+5) is (2x+3)/(x^2+3x+5)

What is the first derivative of ln(x^2+3x+5) ?

The first derivative of ln(x^2+3x+5) is (2x+3)/(x^2+3x+5)

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\frac{d}{d x} (ln (x^{2} + 3 x + 5))

\frac{2 x + 3}{x ^{2} + 3 x + 5}

Solution steps

\frac{d}{d x} (ln (x^{2} + 3 x + 5))

Apply the chain rule:

\frac{1}{x ^{2} + 3 x + 5} \frac{d}{d x} (x^{2} + 3 x + 5)

= \frac{1}{x ^{2} + 3 x + 5} \frac{d}{d x} (x^{2} + 3 x + 5)

\frac{d}{d x} (x^{2} + 3 x + 5) = 2 x + 3

= \frac{1}{x ^{2} + 3 x + 5} (2 x + 3)

Simplify

\frac{1}{x ^{2} + 3 x + 5} (2 x + 3) : \frac{2 x + 3}{x ^{2} + 3 x + 5}

= \frac{2 x + 3}{x ^{2} + 3 x + 5}

What is the derivative of ln(x^2+3x+5) ?
The derivative of ln(x^2+3x+5) is (2x+3)/(x^2+3x+5)
What is the first derivative of ln(x^2+3x+5) ?
The first derivative of ln(x^2+3x+5) is (2x+3)/(x^2+3x+5)