Chain Rule 3.5. Consider: These can all be thought of as composite functions F(g(x)) Derivatives of Composite functions are found using the chain rule.

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Presentation transcript:

Chain Rule 3.5

Consider: These can all be thought of as composite functions F(g(x)) Derivatives of Composite functions are found using the chain rule.

The Chain Rule Consider the composition of two functions f(x) and g(x) given by The formula for the derivative of this composition is known as the chain rule. Chain Rule If y = g(u) and u = f(x) and both of these functions are differentiable, then the composite function y = g[f(x)] is differentiable and Derivative of the outside times derivative of the inside

Example: Find the derivative: This may not always be easy to expand Use the chain Rule! Outer Inner

Find derivative of:

Find:

Find derivative of:

Find Derivative of: Chain Rule allows us to use product rule instead of quotient rule! First Times the derivative of the second Plus the second Times the derivative of the first

More Chain Rule!!!!!! Day 2

Find derivative of: RewriteChain Rule Simplify

Find: Rewrite Chain Rule

Find derivative of: Rewrite Chain Rule Double angle Formula Sin2u = 2sinu * cosu

Find the slope of the tangent line of: