/ x\ cos\E /
cos(E^x)
Let u=exu = e^{x}u=ex.
The derivative of cosine is negative sine:
Then, apply the chain rule. Multiply by ddxex\frac{d}{d x} e^{x}dxdex:
The derivative of exe^{x}ex is itself.
The result of the chain rule is:
Now simplify:
The answer is:
x / x\ -e *sin\E /
/ / x\ x / x\\ x -\cos\E /*e + sin\E //*e
/ / x\ 2*x / x\ / x\ x\ x \- sin\E / + e *sin\E / - 3*cos\E /*e /*e