# Thread: Applications of differentiation

1. ## Applications of differentiation

Find in the domain x greater than equal to 0 and x is less than or equal to 2 Pi the x coordinates of the points on the curve y= e^sinx where the tangent is horizontal.

2. ## Re: Applications of differentiation

Differentiate $y = e^{\sin x}$ using the rule

$\frac{d}{dx}\, e^{f(x)} = f'(x) e^{f(x)}$

and when solving $\frac{dy}{dx} = 0$, note that $e^{\sin x}$ is never zero.

3. ## Re: Applications of differentiation

Originally Posted by fan96
Differentiate $y = e^{\sin x}$ using the rule

$\frac{d}{dx}\, e^{f(x)} = f'(x) e^{f(x)}$

and when solving $\frac{dy}{dx} = 0$, note that $e^{\sin x}$ is never zero.
The solution is Pi/2 and 3pi/2

4. ## Re: Applications of differentiation

wait think about it wats sinpi/2 ? Its 1 so e^1 is 0 ??? no its e same thing with 3pi/2 it becomes -1 so 1/e

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