What is the derivative of 30ln(3x+1) ?

The derivative of 30ln(3x+1) is (90)/(3x+1)

What is the first derivative of 30ln(3x+1) ?

The first derivative of 30ln(3x+1) is (90)/(3x+1)

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derivative of

30 ln (3 x + 1)

\frac{90}{3 x + 1}

Solution steps

\frac{d}{d x} (30 ln (3 x + 1))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 30 \frac{d}{d x} (ln (3 x + 1))

Apply the chain rule:

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

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

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

= 30 \cdot \frac{1}{3 x + 1} \cdot 3

Simplify

30 \cdot \frac{1}{3 x + 1} \cdot 3 : \frac{90}{3 x + 1}

= \frac{90}{3 x + 1}

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What is the derivative of 30ln(3x+1) ?
The derivative of 30ln(3x+1) is (90)/(3x+1)
What is the first derivative of 30ln(3x+1) ?
The first derivative of 30ln(3x+1) is (90)/(3x+1)