Question

Differentiate the following functions with respect to x:-

1. log₇(1og₇ x)

2. log x 2


Expecting Good answer !

Answer 1

Final Answer :
1)
$\frac{1}{ ln(7) ln(x) } \times \frac{1}{x} \\ 2) \frac{1}{ ln(10) } \times \frac{2}{x}$
Here,
ln has log base 'e'

Understanding :
1) Base changing theorem :
Like
$log_{10}( {x}^{2} ) = \frac{ ln( {x}^{2} ) }{ ln(10) }$

Steps :
1) In both questions, first we will change all bases to "e" from 7 to e in first question and from base 10 to 'e'in second question.

2) Then, we know that
Differentiation of
$ln(f(x)) \: \: is \: \frac{1}{f(x)} \times \frac{df(x)}{dx}$


We will apply this chain rule in both questions.

For Calculation see pic

Sorry, for my bad Handwriting,
Try to understand it , if you can't understand then notify me.