If f(x) = esin x, then what is derivative of f(x) ?

  1. (sin x)esin x
  2. (cos x)esin x
  3. (sec x)esin x
  4. (cosec x)esin x

Answer (Detailed Solution Below)

Option 2 : (cos x)esin x
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Detailed Solution

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Concept:

Derivative Rule:

Let y = ef(x) then

\(\rm \dfrac {dy}{dx} = e^{f(x)} \dfrac {d}{dx} f(x)\)

Calculations:

Given, f(x) = esin x

Taking derivative w. r. to x on both side, we get

⇒f'(x) = \(\rm \dfrac {d}{dx}\)(esin x)

⇒f'(x) = esin x \(\rm \dfrac {d}{dx} (\sin x)\)

⇒f'(x) = esin x \(\rm ( \cos x)\)

⇒f'(x) = \(\rm (\cos x)\)esin x 

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