If \( y=\log_{x}(x^{2}+1)\cdot\log_{(x^{2}+1)}x \), then \( \displaystyle\frac{dy}{dx} \) is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( 0 \)
By the change of base rule, the two logarithms are reciprocals of each other:
\( \displaystyle y=\frac{\log(x^{2}+1)}{\log x}\cdot\frac{\log x}{\log(x^{2}+1)} \)
\( y=1 \)
So y is a constant, and
\( \displaystyle \frac{dy}{dx}=0 \)