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NDA 2020
Exam
NDA
Year
2020
Subject
Mathematics
Chapter
Differentiation

NDA 2020 · Mathematics · Differentiation

What is the derivative of ^ -1 x with respect to ^ -1 x ?

What is the derivative of tan⁡−1x\tan ^{-1} x with respect to cot⁡−1x\cot ^{-1} x ?

Options

  1. A-1
  2. B1
  3. C1x2+1\frac{1}{x^2+1}
  4. Dxx2+1\frac{x}{x^2+1}

Correct answer

A. -1

Step-by-step solution

Let y=tan⁡−1xy=\tan ^{-1} x; and z=cot⁡−1xz=\cot ^{-1} x Then, dydx=11+x2\frac{d y}{d x}=\frac{1}{1+x^2} and dzdx=−11+x2\frac{d z}{d x}=-\frac{1}{1+x^2} Now, dydz=dydxdzdx=11+x2−(11+x2)=−1\frac{d y}{d z}=\frac{\frac{d y}{d x}}{\frac{d z}{d x}}=\frac{\frac{1}{1+x^2}}{-\left(\frac{1}{1+x^2}\right)}=-1.
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