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# 4.6b - 4.6b More on Related Rates Sometimes more than two...

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Calculus Section 4.6 Page31 4.6b More on Related Rates Sometimes more than two quantities are changing within a certain relationship. At this point, you must consider the product rule, the quotient rule, and the chain rule when differentiating to express how different rates of change are related. Areas Rectangle: A = lw Find an equation that relates dA dt , dl dt , and dw dt Triangle: A = 1 2 bh Find an equation that relates dA dt , db dt , and dh dt Volumes Cylinder: V = π r 2 h Find an equation that relates dV dt , dr dt , and dh dt Cone: V = 1 3 π r 2 h Find an equation that relates dV dt , dr dt , and dh dt Cone: V = 1 3 π r 2 h Find an equation that relates dV dt and dr dt if h is a constant.

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Page 32 Sphere: V = 4 3 π r 3 Find an equation that relates dV dt and dr dt Rectangular box: V = lwh Find an equation that relates dV dt , dl dt , dw dt , and dh dt Lengths of Sides Right Triangle: x 2 + y 2 = z 2 Find an equation that relates dx dt , dy dt , and dz dt Right Triangle: x 2 + y 2 = z 2 Find an equation that relates dx dt and dz dt if y is a constant. Diagonal of a rectangle:
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4.6b - 4.6b More on Related Rates Sometimes more than two...

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