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Popular >

derivative of ln(x/3 (x-3))

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

f = ln (\frac{x}{3}), g = x - 3

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

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

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

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

Simplify

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

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

Popular Examples

integral of (361)/(x^3-19x^2)

\int \frac{361}{x ^{3} - 19 x ^{2}} d x

derivative of-6sin(x)

\frac{d}{d x} (- 6 sin (x))

derivative of 1/20 e^x+x^6-x^e+e

\frac{d}{d x} (\frac{1}{20} e^{x} + x^{6} - x^{e} + e)

(\partial)/(\partial x)(sin^9(x))

\frac{\partial}{\partial x} (sin^{9} (x))

(\partial)/(\partial y)(y*cos(y-2x))

\frac{\partial}{\partial y} (y \cdot cos (y - 2 x))

Frequently Asked Questions (FAQ)

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