Product & Quotient Rule

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## Product & Quotient Rule

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**Product & Quotient Rule**Higher Order Derivatives**The Product Rule**• Theorem. Let f and g be differentiable functions. Then the derivative of the product fg is • (fg) '(x) = f(x) g '(x) + g(x) f '(x) In other words, first times the derivative of the second plus second times the derivative of the first.**Using the Product Rule**• Example:**Product Rule**• Example:**Product Rule**• Example**Quotient Rule**• Theorem. Let f and g be differentiable functions. Then the derivative of the quotient f/g is In other words, low d high minus high d low over low low.**Quotient Rule**• Example • Find the derivative of**Rewriting Before Differentiating**• Example:**Proof of Derivative of Tangent**• Considering**Differentiating Trig Functions**• y = x – tan x • y = x sec x y’ = x(sec x tan x) + sec x (1) = sec x (x tan x + 1)**Higher Order Derivatives**Applications: Finding Acceleration Due to Gravity Population Growth p. 125 problem 79 Any time we are asked to find the rate at which a rate is changing, this is a second derivative.