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NDA 2017
Exam
NDA
Year
2017
Subject
Mathematics
Chapter
Differentiation

NDA 2017 · Mathematics · Differentiation

What is the derivative of _ 10 (5 x^2+3) with respect to x ?

What is the derivative of log⁡10(5x2+3)withrespecttox?\log _{10} \left(5 \mathrm{x}^2+3\right) with respect to x ?

Options

  1. Axlog⁡10e5x2+3\frac{\mathrm{x} \log _{10} \mathrm{e}}{5 \mathrm{x}^2+3}
  2. B2xlog⁡10e5x2+3\frac{2 \mathrm{x} \log _{10} \mathrm{e}}{5 \mathrm{x}^2+3}
  3. C10xlog⁡10e5x2+3\frac{10 \mathrm{x} \log _{10} \mathrm{e}}{5 \mathrm{x}^2+3}
  4. D10xlog⁡e105x2+3\frac{10 \mathrm{x} \log _e 10}{5 \mathrm{x}^2+3}

Correct answer

C. 10xlog⁡10e5x2+3\frac{10 \mathrm{x} \log _{10} \mathrm{e}}{5 \mathrm{x}^2+3}

Step-by-step solution

y=log⁡10(5x2+3)dydx=ddx(log⁡10(5x2+3))=15x2+3×log⁡10e×10x=10xlog⁡10e5x2+3\begin{aligned} & \mathrm{y}=\log _{10}\left(5 \mathrm{x}^2+3\right) \\ & \frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{d}}{\mathrm{dx}}\left(\log _{10}\left(5 \mathrm{x}^2+3\right)\right)=\frac{1}{5 \mathrm{x}^2+3} \times \log _{10} \mathrm{e} \times 10 \mathrm{x} \\ & =\frac{10 \mathrm{x} \log _{10} \mathrm{e}}{5 \mathrm{x}^2+3}\end{aligned}
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