Exponential and Log Derivatives AP Calculus Unit 3 Day 7 Exponential and Log Derivatives

ARRIVAL PRACTICE Continued

ARRIVAL PRACTICE

g is continuous and differentiable at x = 0 More PRACTICE g is continuous and differentiable at x = 0 g is continuous, but not differentiable at x = 0 g is not continuous, but is differentiable at x = 0 g is not continuous or differentiable at x = 0 Nothing can be said about differentiability at x = 0

4. The position, in feet, of a particle can be described by More PRACTICE 4. The position, in feet, of a particle can be described by the function: . Find the velocity of the particle at t = 2 seconds. (Calculator active)

Today’s topic: Exponential Derivatives

Exponential Rules Easiest derivative!

Think about the implications for The slope of the tangent line at any point on is equal to the y -value at that point. (1,0)

Exponential Rules (PINK SHEET) Easiest derivative! Exponential functions with a base other than “e”. Note: “a” is a number! Using the chain rule (exponent is more than just an “x”)

Examples: Find the derivative:

Examples: Find the derivative:

Logarithmic Derivatives

Logarithmic Rules (PINK SHEET) Basic natural log derivative Log functions with a base other than “e”. Note: “a” is a number! Using the chain rule (inner function is more than just an “x”)

Examples: Find the derivative: