What is the derivative of xln(x/5) ?

The derivative of xln(x/5) is ln(x/5)+1

What is the first derivative of xln(x/5) ?

The first derivative of xln(x/5) is ln(x/5)+1

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\frac{d}{d x} (x ln (\frac{x}{5}))

ln (\frac{x}{5}) + 1

Solution steps

\frac{d}{d x} (x ln (\frac{x}{5}))

Apply the Product Rule:

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

f = x, g = ln (\frac{x}{5})

= \frac{d x}{d x} ln (\frac{x}{5}) + \frac{d}{d x} (ln (\frac{x}{5})) x

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

\frac{d}{d x} (ln (\frac{x}{5})) = \frac{1}{x}

= 1 \cdot ln (\frac{x}{5}) + \frac{1}{x} x

Simplify

1 \cdot ln (\frac{x}{5}) + \frac{1}{x} x : ln (\frac{x}{5}) + 1

= ln (\frac{x}{5}) + 1

What is the derivative of xln(x/5) ?
The derivative of xln(x/5) is ln(x/5)+1
What is the first derivative of xln(x/5) ?
The first derivative of xln(x/5) is ln(x/5)+1