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Mastering Derivatives: Unlocking the Power Rule in Calculus

Join Leibniz and Newton on a journey through the Power Rule. Learn to find derivatives efficiently and tackle polynomial challenges. Discover the Sum and Difference Rules and solve real-world problems. Are you ready to conquer calculus?

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Mastering Derivatives: Unlocking the Power Rule in Calculus

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  1. Computations of the Derivative: The Power Rule Gottfried Leibniz (1646-1716) Sir Isaac Newton (1642-1727)

  2. Find the Derivative of:

  3. What’s going on???? • Write your own rule! On your sheet of paper come up with a rule that can be used to derive polynomials.

  4. Now try doing a lot with a Little!

  5. AND More Fun-ctions to dErive!

  6. Are you ready for a challenge? Do it any way!!!!

  7. Rules: Theorem 3.1 • For any constant c, Theorem 3.2 Theorem 3.3 For any integer n > 0,

  8. DRUM ROLL PLEASE….. Enough, STOP THE DRUM ROLL!!!!! Theorem 3.4 For any real number r,

  9. Sum and Difference Rules • If f(x) and g(x) are differentiable at x and c is any constant, then:

  10. Examples: • Suppose that the height of a skydiver t seconds after jumping from an airplane is given by f(t) = 225 – 20t – 16t2 feet. Find the person’s acceleration at time t. First compute the derivative of this function to find the velocity Second compute the derivative of this function to find the acceleration The speed in the downward direction increases 32 ft/s every second due to gravity.

  11. Given f(x) = x3 – 6x2 + 1 a) Find the equation of the tangent line to the curve at x = 1 y = -9x + 5 b) Find all points where the curve has a horizontal tangent X=0 and x = 4

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