Question

y = log 3x, then dy/dx =?​

Answer 1

Answer:

By Change of Base Formula:  

log

b

x

=

log

a

x

log

a

b

,

y

=

log

3

x

=

ln

x

ln

3

By taking the derivative,

y

'

=

1

x

ln

3

=

1

(

ln

3

)

x

Step-by-step explanation:

Answer 2

Given:

y = log 3x

To find:

$\frac{dy}{dx }$

Solution:

We know that

$\frac{d}{dx} (log \: x) = \frac{1}{x}$

By the differential formula,

$\frac{d}{dx} (log \: 3x) = \frac{1}{3x } \times \frac{d}{dx} (3x) \\ = \frac{1}{3x} \times 3 \\ = \frac{1}{x}$