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Quiz / Weekly #4 Feedback. -More Effort Needed! -Wording of Problems (derivative, slope at a point, slope of tangent line…) -Product / Quotient Rules!!! -Quiz I:g and II:a -Weekly 7 , 8 , 10. The Chain Rule. 4.1.1. The Chain Rule.

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## Quiz / Weekly #4 Feedback

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**Quiz / Weekly #4 Feedback**-More Effort Needed! -Wording of Problems (derivative, slope at a point, slope of tangent line…) -Product / Quotient Rules!!! -Quiz I:g and II:a -Weekly 7 , 8 , 10**The Chain Rule**4.1.1**The Chain Rule**If y = f (u) is a differentiable function of u and u = g(x) is a differentiable function of x, theny= f (g(x)) is a differentiable function of x and or, equivalently,**Identify the inner and outer functions**Composite y = f (g(x)) Inner u = g(x) Outery= f (u) 1. 2. 3. 4.**The General Power Rule**• If , where u is a differentiable function of x and n is a rational number, then or, equivalently,**Homework**• Chain Rule Worksheet**Simplifying Chain Rule**4.1.2**Factoring Out the Least Powers**• Find the Derivative**Factoring Out the Least Powers**• Find the Derivative**Factoring Out the Least Powers**• Find the Derivative**Trig Tangent Line**• Find an equation of the tangent line to the graph of at the point (π, 1). Then determine all values of x in the interval (0, 2π) at which the graph of f has a horizontal tangent.**Homework**• p.153/ 1-11(O) , 21-39 (O) , 59**Guidelines for Implicit Differentiation**• Differentiate both sides of the equation with respect to x. • Collect all terms involving dy / dx on the left side of the equation and move all other terms to the right side of the equation. • Factor dy / dx out of the left side of the equation. • Solve for dy / dx.**Homework**• p.162/ 1-19odd, 49, 51**Example**• Determine the slope of the tangent line to the graph of at the point .**Example**• Determine the slope of the tangent line to the graph of at the point .**Example**• Find the tangent and normal line to the graph given by at the point .**Homework**• p.162/ 21-25odd, 27-30, 31-43odd**Inverse Functions**1.5/3.8**Definition of Inverse Function**• A function g is the inverse function of the function f if for each x in the domain of g. and for each x in the domain of f.**Verifying Inverse Functions**• Show that the functions are inverse functions of each other. and**The Existence of an Inverse Function**• A function has an inverse function if and only if it is one-to-one. • If f is strictly monotonic on its entire domain, then it is one-to-one and therefore has an inverse function.**Existence of an Inverse Function**• Which of the functions has an inverse function?**Finding an Inverse**• Find the inverse function of .**The Derivative of an Inverse Function**• Let f be a function that is differentiable on an interval I. If f has an inverse function g, then g is differentiable at any x for which . Moreover,**Example**• Let . a) What is the value of when x = 3? b) What is the value of when x = 3?**Homework**• p. 44/ 1-6, 7-23odd, 43 • p. 170/ 28, 29bc**The Inverse Trigonometric Functions**Function**Evaluating Inverse Trigonometric Functions**• Evaluate each function.**Using Right Triangles**a) Given y = arcsin x, where , find cos y. b) Given , find tan y.**Homework**3.8 Inverse Trig Review worksheet**Homework**• p. 170/ 1-27odd, 31ab

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