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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

f = x - 4, g = ln (\frac{x}{4})

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

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

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

= 1 \cdot ln (\frac{x}{4}) + \frac{1}{x} (x - 4)

Simplify

1 \cdot ln (\frac{x}{4}) + \frac{1}{x} (x - 4) : ln (\frac{x}{4}) + \frac{x - 4}{x}

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

f (x) = \frac{e ^{x}}{7 x ^{2} + 4}

8 x - 8 x

\int_{0.5}^{3} \frac{sin ( x )}{x} d x

t - 3

y = - 4 cos (x), at x = \frac{π}{2}

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