What is the derivative of ((x-4)/x+ln(x/4)) ?

The derivative of ((x-4)/x+ln(x/4)) is 4/(x^2)+1/x

What is the first derivative of ((x-4)/x+ln(x/4)) ?

The first derivative of ((x-4)/x+ln(x/4)) is 4/(x^2)+1/x

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\frac{d}{d x} (\frac{( x - 4 )}{x} + ln (\frac{x}{4}))

\frac{4}{x ^{2}} + \frac{1}{x}

Solution steps

\frac{d}{d x} (\frac{( x - 4 )}{x} + ln (\frac{x}{4}))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{x - 4}{x}) + \frac{d}{d x} (ln (\frac{x}{4}))

\frac{d}{d x} (\frac{x - 4}{x}) = \frac{4}{x ^{2}}

\frac{d}{d x} (ln (\frac{x}{4})) = \frac{1}{x}

= \frac{4}{x ^{2}} + \frac{1}{x}

\int \frac{1}{x ^{4} + x ^{2}} d x

\frac{\partial}{\partial x} (t^{2} x - t)

\int \frac{x ^{2}}{x ^{4} - 20 x ^{2} - 125} d x

\frac{d}{d x} (5 \cdot 4^{x})

\int e^{(a - b) x} d x

What is the derivative of ((x-4)/x+ln(x/4)) ?
The derivative of ((x-4)/x+ln(x/4)) is 4/(x^2)+1/x
What is the first derivative of ((x-4)/x+ln(x/4)) ?
The first derivative of ((x-4)/x+ln(x/4)) is 4/(x^2)+1/x