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

Derivative of e^sin(x)

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

The graph:

from to

Piecewise:

The solution

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

  1. Let .

  2. The derivative of is itself.

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

    1. The derivative of sine is cosine:

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