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Mathematics · JEE | APPLICATION OF DERIVATIVES

हिन्दी

What is the derivative of \( f(x) = \sin 3x \)?

  1. A
    \( 3\cos 3x \)
  2. B
    \( 3\sin 3x \)
  3. C
    \( \sin 3x \)
  4. D
    \( -3\cos 3x \)
View Answer & Solution

Correct answer · Option A

\( 3\cos 3x \)

Explanation

By chain rule, the derivative of \( \sin 3x \) is \( 3\cos 3x \).

Related questions

In the graph representing local extrema and points of non-differentiability, let \( c_2 \) be a point of local minima and \( c_3 \) be a point of non-differentiability. Which of the following correctly describes the behavior of \( f'(x) \) around \( c_2 \)?→Find the intervals in which the function \( f(x) = 10 - 6x - 2x^2 \) is strictly increasing.→Find the minimum value of the function \( f(x) = x^2 \) for \( x \in \mathbb{R} \).→Given below two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The function \( f(x) = x^3 - 3x^2 + 3x - 100 \) is strictly increasing on \( \mathbb{R} \). Reason (R): If \( f'(x) > 0 \) for all \( x \in \mathbb{R} \), then \( f(x) \) is strictly increasing on \( \mathbb{R} \). In the light of the above statements, choose the correct answer from the options given below:→
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