What is the derivative of (x-5ln((x-5)/(10))) ?

The derivative of (x-5ln((x-5)/(10))) is ln((x-5)/(10))+1

What is the first derivative of (x-5ln((x-5)/(10))) ?

The first derivative of (x-5ln((x-5)/(10))) is ln((x-5)/(10))+1

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\frac{d}{d x} ((x - 5) ln (\frac{x - 5}{10}))

ln (\frac{x - 5}{10}) + 1

Solution steps

\frac{d}{d x} ((x - 5) ln (\frac{x - 5}{10}))

Apply the Product Rule:

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

f = x - 5, g = ln (\frac{x - 5}{10})

= \frac{d}{d x} (x - 5) ln (\frac{x - 5}{10}) + \frac{d}{d x} (ln (\frac{x - 5}{10})) (x - 5)

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

\frac{d}{d x} (ln (\frac{x - 5}{10})) = \frac{1}{x - 5}

= 1 \cdot ln (\frac{x - 5}{10}) + \frac{1}{x - 5} (x - 5)

Simplify

1 \cdot ln (\frac{x - 5}{10}) + \frac{1}{x - 5} (x - 5) : ln (\frac{x - 5}{10}) + 1

= ln (\frac{x - 5}{10}) + 1

\int \frac{1}{x 64 x ^{2} - 5} d x

\int_{- 1}^{1} (0 - y^{2} + 1) d y

12 y^{^{''}} - 12 y^{^{'}} + 30 y = 0

\int \frac{3 x ^{3}}{4 + x ^{8}} d x

\frac{d x}{d y} = 3 x^{2} y^{3}

What is the derivative of (x-5ln((x-5)/(10))) ?
The derivative of (x-5ln((x-5)/(10))) is ln((x-5)/(10))+1
What is the first derivative of (x-5ln((x-5)/(10))) ?
The first derivative of (x-5ln((x-5)/(10))) is ln((x-5)/(10))+1