What is the derivative of x/4 (1+ln(4/x)) ?

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

What is the first derivative of x/4 (1+ln(4/x)) ?

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

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

f = x, g = 1 + ln (\frac{4}{x})

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

\int (5 + x^{4}) sin (\frac{1}{2} x) d x

\int_{2}^{e^{5}} \frac{1}{x} d x

\int cos^{5} (x s i) n^{2} x d x

f (x) = 2 + e^{x}, at x = 1

x \to 2 lim (- x^{2} + 3 x)

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