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Consider the function

slope. Consider the function. We could make a graph of the slope:. Now we connect the dots!. The resulting curve is a cosine curve. slope. We can do the same thing for. The resulting curve is a sine curve that has been reflected about the x-axis. Derivative of y=sinx.

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Consider the function

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  1. slope Consider the function We could make a graph of the slope: Now we connect the dots! The resulting curve is a cosine curve.

  2. slope We can do the same thing for The resulting curve is a sine curve that has been reflected about the x-axis.

  3. Derivative of y=sinx • Use the definition of the derivative To prove the derivative of y=sinx is y’=cosx.

  4. Derivative of y=sinx Shortcut: y’=cosx The proof of the d(cosx) = -sinx is almost identical

  5. product rule: Notice that this is not just the product of two derivatives. This is sometimes memorized as:

  6. Example:

  7. Try this:

  8. Try this:

  9. quotient rule: or

  10. Quotient Rule

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