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

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⁡(ex)\cos{\left(e^{x} \right)} 
cos(E^x)
Detail solution

  1. Let u=exu = e^{x}.

  2. The derivative of cosine is negative sine:

    dducos⁡(u)=−sin⁡(u)\frac{d}{d u} \cos{\left(u \right)} = - \sin{\left(u \right)}

  3. Then, apply the chain rule. Multiply by ddxex\frac{d}{d x} e^{x}:

    1. The derivative of exe^{x} is itself.

    The result of the chain rule is:

    −exsin⁡(ex)- e^{x} \sin{\left(e^{x} \right)}

  4. Now simplify:

    −exsin⁡(ex)- e^{x} \sin{\left(e^{x} \right)}

The answer is:

−exsin⁡(ex)- e^{x} \sin{\left(e^{x} \right)}

The graph
02468-8-6-4-2-1010-5000050000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
  x    / x\
-e *sin\E /
−exsin⁡(ex)- e^{x} \sin{\left(e^{x} \right)}
Simplify
The second derivative [src] 
 /   / x\  x      / x\\  x
-\cos\E /*e  + sin\E //*e
−(excos⁡(ex)+sin⁡(ex))ex- \left(e^{x} \cos{\left(e^{x} \right)} + \sin{\left(e^{x} \right)}\right) e^{x}
Simplify
The third derivative [src] 
/     / x\    2*x    / x\        / x\  x\  x
\- sin\E / + e   *sin\E / - 3*cos\E /*e /*e
(e2xsin⁡(ex)−3excos⁡(ex)−sin⁡(ex))ex\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}
Simplify
The graph
Derivative of cos(e^x)
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