What is the derivative of 40ln(3x+1) ?

The derivative of 40ln(3x+1) is (120)/(3x+1)

What is the first derivative of 40ln(3x+1) ?

The first derivative of 40ln(3x+1) is (120)/(3x+1)

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derivative of

40 ln (3 x + 1)

\frac{120}{3 x + 1}

Solution steps

\frac{d}{d x} (40 ln (3 x + 1))

Take the constant out:

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

= 40 \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

= 40 \cdot \frac{1}{3 x + 1} \cdot 3

Simplify

40 \cdot \frac{1}{3 x + 1} \cdot 3 : \frac{120}{3 x + 1}

= \frac{120}{3 x + 1}

\frac{1}{2} (e^{x} + e^{- x})

x^{2} - x - 6, - 4

y = 8

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What is the derivative of 40ln(3x+1) ?
The derivative of 40ln(3x+1) is (120)/(3x+1)
What is the first derivative of 40ln(3x+1) ?
The first derivative of 40ln(3x+1) is (120)/(3x+1)