MATA32H3 Study Guide - Quiz Guide: Quotient Rule
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MATA32H3 Full Course Notes
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Key: differentiate y = ln x x2 . This is quotient rule: bottom times derivative of the top, minus top times derivative of the bottom, over the bottom squared. In this case: dy dx x2 1 x (ln x) 2x x4 x 2x ln x x4. Continued on reverse: find f(cid:48)(x) if f (x) = (cid:16) (cid:17)3 ln(4x 10) Differentiating this in the usual way would give 3(something)2, but by chain rule we have to adjust this by multiplying by the derivative of the some- thing. In our case, the something is ln(4x 10). This looks like ln(blah), so we expect to get something like 1 blah after we differ- entiate. Again by chain rule, we need to adjust our expectation by multiplying by the derivative of blah. Our blah is 4x 10, so the derivative is just 4. Putting all this together: f(cid:48)(x) = 3(cid:0)ln(4x 10)(cid:1)2 .
