Bases other than e ap calc notesPresentation Transcript
No warm up today.
5.5 Bases other than e
Objective: To take the derivative and integrals of other exponential functions.
y = ax has a constant base and variable exponent.
YOU CANNOT USE THE POWER RULE! WHY?
You must use logarithmic differentiation or memorize a
Ex1. y = 2
Ex2: y = 5
Do you notice a pattern with the answers???????
If y = au, then y’ = (au)(lna)(u’)
How is this the same for y = eu?
But WAIT!! This short-cut will only work if
the base is a constant.
Remember: If y = variable base variable exponent you MUST use
log differentiation. The following have NO shortcut.
1) y = xsinx
Derivative of y = log a x
If y = log a u, then y’ =
u ln a
Find y’ for each of the following.
1. y = log5 x2
2. y = log3 7x
Integrals of bases other than e.
1. 2 x dx
Be aware, you may have to use u-substitution!!
2. 25 x dx
1. x 5