Function a^x Flashcards
1
Q
how to prove that derivative of a^x is lna x a^x
A
Step 1: raise y=a^x to e^ln(a) Step 2: differentiate this using exponential law Step 3: lna x a^x Step 4: as first line says y=e^lna^x Step 5: sub y in, as y=ax
lna x a^x as required.
2
Q
What is the shape of the a^x curve?
A
- Never goes into bottom two quadrants
- Starts on left goes through (0,1) and grows upward.
3
Q
What is the integral of a^x
A
a^x/lna +C
