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Popular >

derivative of ln(x/2 (x-2))

Solution

\frac{d}{d x} (ln (\frac{x}{2}) (x - 2))

Solution

\frac{x - 2}{x} + ln (\frac{x}{2})

Solution steps

\frac{d}{d x} (ln (\frac{x}{2}) (x - 2))

Apply the Product Rule:

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

f = ln (\frac{x}{2}), g = x - 2

= \frac{d}{d x} (ln (\frac{x}{2})) (x - 2) + \frac{d}{d x} (x - 2) ln (\frac{x}{2})

\frac{d}{d x} (ln (\frac{x}{2})) = \frac{1}{x}

\frac{d}{d x} (x - 2) = 1

= \frac{1}{x} (x - 2) + 1 \cdot ln (\frac{x}{2})

Simplify

\frac{1}{x} (x - 2) + 1 \cdot ln (\frac{x}{2}) : \frac{x - 2}{x} + ln (\frac{x}{2})

= \frac{x - 2}{x} + ln (\frac{x}{2})

Graph

Popular Examples

limit as x approaches 0-of (x+10)/(x^2)

x \to 0 - lim (\frac{x + 10}{x ^{2}})

integral of (8x^4+4x^3-6x^2-4x+5)

\int (8 x^{4} + 4 x^{3} - 6 x^{2} - 4 x + 5) d x

derivative of \sqrt[5]{x}+2sqrt(x^5)

\frac{d}{d x} (5 x + 2 x^{5})

derivative of f(x)=(5x^3+6x^2+4)^8 derivative of

f (x) = (5 x^{3} + 6 x^{2} + 4)^{8}

tangent of y=sin(sin(x)),(2pi,0)tangent of

y = sin (sin (x)), (2 π, 0)

Frequently Asked Questions (FAQ)

What is the derivative of ln(x/2 (x-2)) ?
The derivative of ln(x/2 (x-2)) is (x-2)/x+ln(x/2)
What is the first derivative of ln(x/2 (x-2)) ?
The first derivative of ln(x/2 (x-2)) is (x-2)/x+ln(x/2)