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

Question

Question

Answer 1

Concept:

Derivative Rule:

Let y = ef(x) then

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

Calculations:

Given, f(x) = ecos x

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

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

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

⇒ f'(x) = ecos x (- sin x)

⇒ f'(x) = (- sin x)ecos x

Hence, if f(x) = ecos x, then the derivative of f(x) is (- sin x)ecos x .