Differentiation Question 317
Question: Derivative of the function $ f(x)={\log_5}({\log_7}x) $ , $ x>7 $ is
[Orissa JEE 2002]
Options:
A) $ \frac{1}{x(In\text{5)(In}\text{7)(lo}{g_7}x)} $
B) $ \frac{1}{x(ln\text{5)(ln}\text{7)}} $
C) $ \frac{1}{x(Inx)} $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ f(x)={\log_5}({\log_7}x) $
Therefore $ f(x)={\log_5}( \frac{{\log _{e}}x}{{\log _{e}}7} ) $
Therefore $ f(x)={\log_5}{\log _{e}}x-{\log_5}{\log _{e}}7 $
Therefore $ f(x)=\frac{{\log _{e}}{\log _{e}}x}{{\log _{e}}5}-{\log_5}{\log _{e}}7 $
$ {f}’(x)=\frac{1}{x{\log _{e}}x\log 5}-0 $
$ {f}’(x)=\frac{1}{x{\log _{e}}x\frac{{\log _{e}}5}{{\log _{e}}7}{\log _{e}}7} $
$ =\frac{1}{x(\ln 5)(\ln 7)({\log_7}x)} $ .
BETA
