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

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

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

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

f (x) = \frac{x ^{2} - 10 x + 25}{x - 5}

(9.11) (- 8.9)

\frac{\partial}{\partial x} (4 y x)

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

\frac{d}{d x} (4 x - 3 x^{2})

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