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4.2:Derivatives of Products and Quotients

4.2:Derivatives of Products and Quotients. Objectives : Students will be able to… U se and apply the product and quotient rule for differentiation. The Product Rule.

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4.2:Derivatives of Products and Quotients

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  1. 4.2:Derivatives of Products and Quotients Objectives: Students will be able to… Use and apply the product and quotient rule for differentiation

  2. The Product Rule The derivative of the product of 2 functions is the first function times the derivative of the second, plus the second function times the derivative of the first. Let f(x) = u(x)∙v(x) (u’(x) and v’(x) exist) f’(x) = u(x)∙v’(x) + v(x)∙u’(x) Example: Find f’(x) if f(x) = (2x+3)(x2-4) HOW ELSE COULD YOU HAVE DONE THIS?

  3. USING THE PRODUCT RULE, FIND THE DERIVATIVE OF THE FOLLOWING FUNCTIONS. 1. 2. 3. 4.

  4. QUOTIENT RULE The derivative of a quotient is the denominator times the derivative of the numerator, minus the numerator times the derivative of the denominator, all divided by the square of the denominator. Let f(x) = , v(x) ≠ 0, v’(x) and u’(x) exist f’(x) = Be careful …Use parenthesis when subtracting function in numerator. Be aware of signs!

  5. Find f’(x) if f(x) =

  6. Use the quotient rule to find the derivatives. 1. 2.

  7. Find the derivative. 1. 2.

  8. Find the equation for the tangent line to the curve at (1,2)

  9. Applications of Derivative • Position function: s(t) • Velocity: rate of change of the position with respect to time: v(t) = s’(t) • Velocity gives speed as well as direction • Speed : | v(t) | • Acceleration: rate of change of velocity with respect to time: a(t) = v’(t) = s’’(t)

  10. An object is slowing down when…. velocity and acceleration are opposite signs • An object is speeding up when….. velocity and acceleration are the same sign

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