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Damon M


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April 3, 2013








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Luckily, the process becomes shorter when you use binomial expansion, but what about the function, h(x) = (x3 + x2 + x + 1)5? You can’t use binomial expansion, so it becomes extremely tedious. And in the case of h(x) = sin(5x), as well as in the case of h(x) = (ex + ln(x))7, you cannot simply rely simply on rules you know already, like the power rule and the rules for differentiating trigonometric, exponential, and logarithmic functions...
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You need to use the “chain rule.” The Chain Rule: If f is differentiable at the point u = g(x), and g is differentiable at x, then the composite function (f o g)(x) = f(g(x)) is differentiable at x, and (f o g)?(x) = f? (g(x)) ? g?(x) In Leibniz notation, if y = f(u) and u = g(x), then where dy/du is evaluated at u = g(x)...
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