What are the formulas for the derivatives of e^x and ln(x)? How do the formulas

Question

1. What are the formulas for the derivatives of e^x and ln(x)?
2. How do the formulas change when the base is other than e?
3. How can we use these formulas to determine the derivatives of more complex functions involving e^x and ln(x)?
4. What role do the rules for expanding logarithmic functions play in making it easier to find derivatives of complex logarithmic functions?
5. What is L'Hospitals Rule?
6. What conditions must be met in order to make use of it?
7. How do we use it to find a limit?
8. What real-world applications can you find involving exponential and logarithmic functions?
9. Explain how you would use derivatives to explore those applications.

Explanation / Answer

1)for e^x it is e^x and 1/x for lnx

2)for a^x it is a^xlna , d/dx (log a x)=1/xlna

3)depends on the question

4)because on expanding it gives a polynomial

5)lim f(x)/g(x)=lim f'(x)/g'(x)

6)when lim f(x) and lim(gx) are both 0 or are both +- infinity

7)by taking derivatives

8)t1/2 of a catalyst

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