What is the derivative of ln((1+3x)^2) ?

The derivative of ln((1+3x)^2) is 6/(1+3x)

What is the first derivative of ln((1+3x)^2) ?

The first derivative of ln((1+3x)^2) is 6/(1+3x)

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derivative of

ln ((1 + 3 x)^{2})

\frac{6}{1 + 3 x}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{6}{1 + 3 x}

3 t + 4

3 t - 1

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

\frac{d}{d z} (z^{3} + i)

\frac{3 x}{5}

What is the derivative of ln((1+3x)^2) ?
The derivative of ln((1+3x)^2) is 6/(1+3x)
What is the first derivative of ln((1+3x)^2) ?
The first derivative of ln((1+3x)^2) is 6/(1+3x)