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

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

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

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

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derivative of

ln (x^{3} + 3 x)

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d x}{d y} = 5 x + y

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

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

\int (x - 2) d x

\int_{0}^{1} x cos (2 x^{2} + 7) d x

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