Resolved: "How do you find the derivative of y=ln⁡(5x)?"

Karen Simpson

Answered question

2021-12-18

How do you find the derivative of

y = \ln (5 x)

Answer & Explanation

Louis Page

Beginner2021-12-19Added 34 answers

Suppose,

y = \ln (b (x))

then using Chain Rule,

y^{'} = \frac{1}{b (x)} \cdot {(b (x))}^{'}

Similarly following for the above function yields,

y^{'} = \frac{1}{5 x} \cdot {(5 x)}^{'}

y^{'} = \frac{1}{5 x} \cdot 5

y^{'} = \frac{1}{x}

scomparve5j

Beginner2021-12-20Added 38 answers

A student comfortable with the natural logarithm function and its properties might think of this:
One could reason as follows:

y = \ln (5 x) = \ln (5) + \ln (x)

But

\ln (5)

is a constant, so its derivative is 0
Therefore,

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

RizerMix

Expert2021-12-29Added 656 answers

Using the Chain Rule you'll get:
$y^{'} = \frac{1}{5 x} \cdot 5 = \frac{1}{x}$
(Derive $\ln$ as it is and then multiply by the derivative of the argument, 5x).

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