Derivatives and Integrals of Natural Logarithms 5-B

Natural Logarithms Natural logarithm is the logarithm with base e , where e≈2.71828182846 1) Find

Properties of Logarithms b) c) d) e)

Graph of y = ln x Domain (0,∞) and Range (-∞,∞) The function is continuous and increasing The graph is concave down

Derivative of Natural Logs (ln) General: Chain Rule: Let u be a differentiable function of x such that Absolute Value:

2) Find the derivative of

Find the derivative of

4.) Find the derivative of rewrite differentiate and simplify

5) Find the derivative of

Find the derivative of

Solve using Logarithmic Differentiation 1. Take the ln of both sides 2. Use logarithmic properties 3. Differentiate 4. Solve for y’ 5. Substitute for y 6. Simplify

7) Find the derivative of

Remember If y = ln(x), then Therefore

Integration Rule for ln Let u be a differentiable function in terms of x and du = u’dx

8.) Find the antiderivative of

9) Evaluate

10) Evaluate

Home Work Derivatives and Integrals of logarithms worksheet 5-B Use a section header for each of the topics, so there is a clear transition to the audience. Derivatives and Integrals of logarithms worksheet 5-B