If f(x) = g(x)∙ h(x) then f’(x) = g’(x)∙h(x) + g(x)∙h’(x)

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Presentation transcript:

If f(x) = g(x)∙ h(x) then f’(x) = g’(x)∙h(x) + g(x)∙h’(x) Calculus Section 3.5 Use the Product and Quotient Rules to find derivatives Consider: f(x) = x3 and g(x) = x2∙x are equivalent functions. f’(x) = 3x2. How is g’(x) calculated? Can you take the derivative of each factor? g’(x) = (2x)(1) ??? No! Product Rule: If f(x) = g(x)∙ h(x) then f’(x) = g’(x)∙h(x) + g(x)∙h’(x) Find the f’(x) if f(x) = (4x+5)(2x-3)

Find the derivative y = (1/x)(2x2 + 4x – 3)

Quotient Rule If f(x) = g(x) then f’(x) = g’(x)∙h(x) – g(x)∙h’(x) h(x) [h(x)]2 Find the derivative of f(x) = 2x2 + 3x + 1 x + 4

Find the derivative y = 3x2 – 4x x2+7x+1 f(x) = (3x+4)(5x-6) x2 + 2x + 1 y = x2 8

Find the slope of a function at a given point using a calculator TI 84 MATH nDeriv(<function,variable,value> ENTER TI Nspire Menu Calculus Numerical Deriv at pt Variable X Value <value of x> 1st Deriv ( x2 - 5x +3) x=2 Find the slope of f(x) = x2 - 5x + 3 at(2,-3) nDeriv(x2 - 5x + 3 ,x,2) -1

assignment Page 144 Problems 2 –46 even