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e^cos(x)
The derivative of the function/ e^cos(x)

Derivative of e^cos(x)

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 cos(x)
E
$$e^{\cos{\left(x \right)}}$$ 
E^cos(x)
Detail solution

  1. Let .

  2. The derivative of is itself.

  3. Then, apply the chain rule. Multiply by :

    1. The derivative of cosine is negative sine:

    The result of the chain rule is:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
  cos(x)       
-e      *sin(x)
$$- e^{\cos{\left(x \right)}} \sin{\left(x \right)}$$
Simplify
The second derivative [src] 
/   2            \  cos(x)
\sin (x) - cos(x)/*e
$$\left(\sin^{2}{\left(x \right)} - \cos{\left(x \right)}\right) e^{\cos{\left(x \right)}}$$
Simplify
The third derivative [src] 
/       2              \  cos(x)       
\1 - sin (x) + 3*cos(x)/*e      *sin(x)
$$\left(- \sin^{2}{\left(x \right)} + 3 \cos{\left(x \right)} + 1\right) e^{\cos{\left(x \right)}} \sin{\left(x \right)}$$
Simplify
The graph
Derivative of e^cos(x)
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