Derivatives of Exponential Functions

This one is easy:

d/dx(e^u) = e^u du/dx

For example:

y = e^5x

dy/dx = e^5x*5x = 5xe^5x

Now try these. Take dy/dx:

1. y = e^(2x+1)

2. y = e^sinx

dy/dx = cos x e^sinx

3. y = e^{x^^2}Note: this is e to the x squared power.