If y=log_10⁡x+log_x⁡10+log_x⁡x+log_10⁡10, then dy/dx is equal to

Correct answer: (A) 1/(xlog_e⁡10)-(log_e⁡10)/(xlog^(e⁡x2)). y=log_10⁡x+log_x⁡10+log_x⁡x+log_10⁡10 =log_10⁡x+(log_e⁡10)/log_ex+1+1 ⇒ dy/dx=1/xlog_10⁡e-(log_e⁡10)/(xlog^(e⁡x2))

Q3 / 46 · NTA Abhyas (JEE Main) 2020 · Mathematics · Differentiation

If $y = \log_{10} x + \log_{x} 10 + \log_{x} x + \log_{10} 10,$ then $\frac{d y}{d x}$ is equal to

Correct answer
A
$\frac{1}{x \log_{e} 10} - \frac{\log_{e} 10}{x {(\log_{e} x)}^{2}}$
B
$\frac{1}{x \log_{e} 10} - \frac{1}{x \log_{10} e}$
C
$\frac{1}{x \log_{e} 10} - \frac{\log_{e} 10}{x (\log_{e} x)}$
D
None of these

Solution

y = \log_{10} x + \log_{x} 10 + \log_{x} x + \log_{10} 10

= \log_{10} x + \frac{\log_{e} 10}{\log_{e} x} + 1 + 1

\Rightarrow

\frac{d y}{d x} = \frac{1}{x} \log_{10} e - \frac{\log_{e} 10}{x {(\log_{e} x)}^{2}}

Hence, the correct answer is option: 'A'.

If y=log10⁡x+logx⁡10+logx⁡x+log10⁡10, then dydx is equal to

Solution

More Differentiation Questions

If $y = \log_{10} x + \log_{x} 10 + \log_{x} x + \log_{10} 10,$ then $\frac{d y}{d x}$ is equal to