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Popular >

derivative of (3x+1ln(x-1))

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 3 x + 1, g = ln (x - 1)

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

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

\frac{d}{d x} (ln (x - 1)) = \frac{1}{x - 1}

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

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

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

Graph

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Frequently Asked Questions (FAQ)

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