What is the derivative of ln(1+3x) ?

The derivative of ln(1+3x) is 3/(1+3x)

What is the first derivative of ln(1+3x) ?

The first derivative of ln(1+3x) is 3/(1+3x)

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

\frac{3}{1 + 3 x}

Solution steps

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

Apply the chain rule:

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

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

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

= \frac{1}{1 + 3 x} \cdot 3

Simplify

\frac{1}{1 + 3 x} \cdot 3 : \frac{3}{1 + 3 x}

= \frac{3}{1 + 3 x}

\int 12 x^{3} - 4 x d x

(1 + t) (2 t^{2} - 5)

f (x) = (\frac{4 x ^{2}}{2 - x})^{3}

\frac{11 - 3}{p - 1}

\frac{\partial}{\partial x} (y^{\frac{x}{z}})

What is the derivative of ln(1+3x) ?
The derivative of ln(1+3x) is 3/(1+3x)
What is the first derivative of ln(1+3x) ?
The first derivative of ln(1+3x) is 3/(1+3x)