# L12 - Lecture 12 Product Quotient Chain Rule Given any...

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Lecture 12 — Product, Quotient, Chain Rule Given any differentiable functions, we have seen that it is a simple task to differentiate their sum. We now vastly increase the pool of functions that we can differentiate with the use of a few simple rules for computing the derivatives of products, quotients, and compositions of such functions. Product Rule If two functions f and g are differentiable at x , then fg is differerentiable at x and d dx f ( x ) g ( x ) = Sketch of Proof:

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Find the equation of the tangent line to the graph of the function S ( θ ) = θ sin(2 θ ) when θ = π 4 . The graph of the function f ( x ) = x 2 - 6 e 2 x is shown; what x coordinates correspond to points A and B on the graph ?
Quotient Rule If two functions f and g are differentiable at x and g ( x ) 6 = 0 , then f g is differerentiable at x and d dx f ( x ) g ( x ) = Proof: d dx 1 g ( x ) = lim t x 1 g ( t ) - 1 g ( x ) t - x = Thus, d dx f ( x ) g ( x ) = d dx f ( x ) · 1 g ( x ) =

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Find d dx e x x Find d dt ( t - 2) 2 t 2 - 2
d

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L12 - Lecture 12 Product Quotient Chain Rule Given any...

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