What is the derivative of ln(x^2+14x+55) ?

The derivative of ln(x^2+14x+55) is (2x+14)/(x^2+14x+55)

What is the first derivative of ln(x^2+14x+55) ?

The first derivative of ln(x^2+14x+55) is (2x+14)/(x^2+14x+55)

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\frac{d}{d x} (ln (x^{2} + 14 x + 55))

\frac{2 x + 14}{x ^{2} + 14 x + 55}

Solution steps

\frac{d}{d x} (ln (x^{2} + 14 x + 55))

Apply the chain rule:

\frac{1}{x ^{2} + 14 x + 55} \frac{d}{d x} (x^{2} + 14 x + 55)

= \frac{1}{x ^{2} + 14 x + 55} \frac{d}{d x} (x^{2} + 14 x + 55)

\frac{d}{d x} (x^{2} + 14 x + 55) = 2 x + 14

= \frac{1}{x ^{2} + 14 x + 55} (2 x + 14)

Simplify

\frac{1}{x ^{2} + 14 x + 55} (2 x + 14) : \frac{2 x + 14}{x ^{2} + 14 x + 55}

= \frac{2 x + 14}{x ^{2} + 14 x + 55}

\frac{4 t}{4 + t}

x \to 4 lim (x + 4)

\int - 2 x ln (x) d x

\int - 2 x^{3} d x

\frac{d}{d x} (2 arctan (x))

What is the derivative of ln(x^2+14x+55) ?
The derivative of ln(x^2+14x+55) is (2x+14)/(x^2+14x+55)
What is the first derivative of ln(x^2+14x+55) ?
The first derivative of ln(x^2+14x+55) is (2x+14)/(x^2+14x+55)