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NDA 2018
Exam
NDA
Year
2018
Subject
Mathematics
Chapter
Differentiation

NDA 2018 · Mathematics · Differentiation

If f(x) is an even function, where f(x) ≠ 0 , then which one of the...

If f(x)f(x) is an even function, where f(x)≠0f(x) \neq 0, then which one of the following is correct?

Options

  1. A\mathrmf′(x)\mathrmf^{\prime}(\mathrm{x}) is an even function
  2. Bf′(x)f^{\prime}(x) is an odd function
  3. Cf′(x)f^{\prime}(x) may be an even or odd function depending on the type of function
  4. D\mathrmf′(x)\mathrmf^{\prime}(\mathrm{x}) is a constant function

Correct answer

B. f′(x)f^{\prime}(x) is an odd function

Step-by-step solution

f(x)\mathrm{f}(\mathrm{x}) is an even function. Let's see some examples (1)Iff(x)=cos⁡xIf f(x)=\cos x, which is even function, f′(x)=−sin⁡xf^{\prime}(\mathrm{x})=-\sin \mathrm{x}, which is odd function. (2)Iff(x)=x2If f(x)=x^2, which is even function, f′(x)=2xf^{\prime}(\mathrm{x})=2 \mathrm{x}, which is odd function.
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