Mister Exam

Derivative of cos(e^x)

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

The graph:

from to

Piecewise:

The solution

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

  2. The derivative of cosine is negative sine:

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

    1. The derivative of is itself.

    The result of the chain rule is:

  4. Now simplify:


The answer is:

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