NTA Abhyas 2020
- Exam
- NTA Abhyas
- Year
- 2020
- Subject
- Mathematics
- Chapter
- Differentiation
NTA Abhyas 2020 · Mathematics · Differentiation
The differential coefficient of _ 10 x with respect to _ x 10 is
The differential coefficient of with respect to is
Options
- A
- B- {\left(\log_{10} x\right)}^{2}
- C{\left(\log_{\mathrm{x}}10\right)}^{2}
- D
Correct answer
B. - {\left(\log_{10} x\right)}^{2}
Step-by-step solution
Let,& and
and
Now,
and \dfrac{dv}{dx} = \log_{\mathrm{e}} 10 \left[\dfrac{- 1}{x{ \left(\log_{\mathrm{e}} x\right)}^{2}}\right]
= \dfrac{- {\left(\log_{\mathrm{e}} x\right)}^{2}}{{\left(\log_{\mathrm{e}} 10\right)}^{2}} = - {\left(\dfrac{\log_{\mathrm{e}} x}{\log_{\mathrm{e}} 10}\right)}^{2}
and
Now,
and \dfrac{dv}{dx} = \log_{\mathrm{e}} 10 \left[\dfrac{- 1}{x{ \left(\log_{\mathrm{e}} x\right)}^{2}}\right]
= \dfrac{- {\left(\log_{\mathrm{e}} x\right)}^{2}}{{\left(\log_{\mathrm{e}} 10\right)}^{2}} = - {\left(\dfrac{\log_{\mathrm{e}} x}{\log_{\mathrm{e}} 10}\right)}^{2}