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NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Differentiation

NDA 2022 · Mathematics · Differentiation

If y= x x^2-16 2 -8 |x+ x^2-16 | , then what is (d y)/(d x) equal...

If y=xx2−162−8ln⁡∣x+x2−16∣y=\frac{x \sqrt{x^2-16}}{2}-8 \ln \left|x+\sqrt{x^2-16}\right|, then what is dydx\frac{d y}{d x} equal to?

Options

  1. Axx2−16x \sqrt{x^2-16}
  2. Bx−x2−16x-\sqrt{x^2-16}
  3. Cx2−16\sqrt{x^2-16}
  4. D4x2−164 \sqrt{x^2-16}

Correct answer

C. x2−16\sqrt{x^2-16}

Step-by-step solution

WehaveWe have∫x2−a2dx=x2x2−a2−a22ln⁡∣x+x2−a2∣∴dydx=x2−16\begin{aligned} & \int \sqrt{x^2-a^2} d x=\frac{x}{2} \sqrt{x^2-a^2}-\frac{a^2}{2} \ln \left|x+\sqrt{x^2-a^2}\right| \\ & \therefore \frac{d y}{d x}=\sqrt{x^2-16} \end{aligned}$$
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