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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Differentiation

NDA 2013 · Mathematics · Differentiation

If y=x^x , what is (d y)/(d x) at x=1 equal to ?

If y=xxy=x^x, what is dydx\frac{d y}{d x} at x=1x=1 equal to ?

Options

  1. A00
  2. B11
  3. C−1-1
  4. D22

Correct answer

B. 11

Step-by-step solution

y=xx⇒ln⁡y=xln⁡xy=x^x \quad \Rightarrow \quad \ln y=x \ln x1y⋅dydx=1+ln⁡xdydx=yln⁡exdydx∣x=1=1⋅ln⁡e=1\begin{aligned} \frac{1}{y} \cdot \frac{d y}{d x} & =1+\ln x \\ \frac{d y}{d x} & =y \ln e x \\ \left.\frac{d y}{d x}\right|_{x=1} & =1 \cdot \ln e=1\end{aligned}$$
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