What is the derivative of ln(x^3+3x^2+5x+6) ?

The derivative of ln(x^3+3x^2+5x+6) is (3x^2+6x+5)/(x^3+3x^2+5x+6)

What is the first derivative of ln(x^3+3x^2+5x+6) ?

The first derivative of ln(x^3+3x^2+5x+6) is (3x^2+6x+5)/(x^3+3x^2+5x+6)

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derivative of

ln (x^{3} + 3 x^{2} + 5 x + 6)

\frac{3 x ^{2} + 6 x + 5}{x ^{3} + 3 x ^{2} + 5 x + 6}

Solution steps

\frac{d}{d x} (ln (x^{3} + 3 x^{2} + 5 x + 6))

Apply the chain rule:

\frac{1}{x ^{3} + 3 x ^{2} + 5 x + 6} \frac{d}{d x} (x^{3} + 3 x^{2} + 5 x + 6)

= \frac{1}{x ^{3} + 3 x ^{2} + 5 x + 6} \frac{d}{d x} (x^{3} + 3 x^{2} + 5 x + 6)

\frac{d}{d x} (x^{3} + 3 x^{2} + 5 x + 6) = 3 x^{2} + 6 x + 5

= \frac{1}{x ^{3} + 3 x ^{2} + 5 x + 6} (3 x^{2} + 6 x + 5)

Simplify

\frac{1}{x ^{3} + 3 x ^{2} + 5 x + 6} (3 x^{2} + 6 x + 5) : \frac{3 x ^{2} + 6 x + 5}{x ^{3} + 3 x ^{2} + 5 x + 6}

= \frac{3 x ^{2} + 6 x + 5}{x ^{3} + 3 x ^{2} + 5 x + 6}

\frac{d}{d x} (2 x y - 1)

x \to 3 lim (2 x - 8)

\frac{d}{d x} (\frac{600 x}{2 x ^{2} + 25})

\int \frac{8 x ^{2}}{4 x + 6} d x

\int 9 t^{4} + 4 t^{2} d t

What is the derivative of ln(x^3+3x^2+5x+6) ?
The derivative of ln(x^3+3x^2+5x+6) is (3x^2+6x+5)/(x^3+3x^2+5x+6)
What is the first derivative of ln(x^3+3x^2+5x+6) ?
The first derivative of ln(x^3+3x^2+5x+6) is (3x^2+6x+5)/(x^3+3x^2+5x+6)