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

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

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

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

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

Example:

Try this:

quotient rule: or

Quotient Rule