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}

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

dy/dx = 2x e^{x^^2}