# How do you find the derivative of y=ln(5x)?

Then teach the underlying concepts
Don't copy without citing sources
preview
?

Write a one sentence answer...

#### Explanation

Explain in detail...

#### Explanation:

I want someone to double check my answer

Describe your changes (optional) 200

35
Jim H Share
Mar 14, 2015

A student comfortable with the natural logarithm function and its properties might think of this:

One could reason as follows:
$y = \ln \left(5 x\right) = \ln \left(5\right) + \ln \left(x\right)$.

But $\ln \left(5\right)$ is a constant, so its derivative is $0$.

Therefore, $\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{d}{\mathrm{dx}} \left(\ln 5 + \ln x\right) = \frac{d}{\mathrm{dx}} \left(\ln x\right) = \frac{1}{x}$.

Then teach the underlying concepts
Don't copy without citing sources
preview
?

Write a one sentence answer...

#### Explanation

Explain in detail...

#### Explanation:

I want someone to double check my answer

Describe your changes (optional) 200

8
Gaurav Share
Jul 29, 2014

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

Explanation

Suppose, $y = \ln \left(b \left(x\right)\right)$

then using Chain Rule,

$y ' = \frac{1}{b \left(x\right)} \cdot \left(b \left(x\right)\right) '$

Similarly following for the above function yields,

$y ' = \frac{1}{5 x} \cdot \left(5 x\right) '$

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

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

Then teach the underlying concepts
Don't copy without citing sources
preview
?

Write a one sentence answer...

#### Explanation

Explain in detail...

#### Explanation:

I want someone to double check my answer

Describe your changes (optional) 200

2
Gió Share
Mar 24, 2015

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, $5 x$).

##### Just asked! See more
• 13 minutes ago
• 18 minutes ago
• 22 minutes ago
• 22 minutes ago
• 3 minutes ago
• 5 minutes ago
• 6 minutes ago
• 6 minutes ago
• 8 minutes ago
• 11 minutes ago
• 13 minutes ago
• 18 minutes ago
• 22 minutes ago
• 22 minutes ago