AP Calculus BC September 12, 2016

Entry Task What is f’(x) 𝑓 𝑥 =cos⁡(9 𝑥 2 )

hOMEWORK

Learning Targets I can determine the derivative of functions using Implicit differentiation I correctly solved problems involving the derivative of functions.

The Derivative The derivative of f at x is given by 𝑓 ′ 𝑥 = lim ℎ →0 𝑓 𝑥+ℎ −𝑓 𝑥 ℎ provided that the limit exists. The derivative of f at x is the slope of the tangent line through x.

Rules for Differentiation You can use the definition of a limit to derive many basic rules for differentiation: The Constant Rule The Power Rule The Constant Multiple Rule The Sum and Difference Rules The Product and Quotient Rules Derivatives of Trigonometric Functions Chain Rule

Implicit Differentiation Functions can be defined in explicit form: 𝑦 = 3𝑥2 – 2𝑠𝑖𝑛𝑥 Or in implicit form: 𝑥2𝑦 + 𝑥𝑦 − 3𝑦2 = 4 We can use the Chain Rule to find the derivative of implicitly defined functions.

Find the derivative in terms of x 3 𝑦 2 𝑥+3𝑦 𝑦 3 + 𝑦 2 −4𝑦 − 𝑥 2 =4

Find the slope of the graph 3 𝑥 2 + 𝑦 2 2 =100𝑥𝑦 at point (3,1)

The Second Derivative Given 𝑥 2 + 𝑦 2 =25 find 𝑑 2 𝑦 𝑑 𝑥 2 Evaluate the first and second derivative at (-3,4)

Learning Targets I can determine the derivative of functions using Implicit differentiation I correctly solved problems involving the derivative of functions.

Assignment #8 §2.5 pp. 146-147: 9, 13, 27, 31, 37, 47, 53, 57, 65