![]() ![]() We have a sum of three functions, not just two.īeing explicit about the fact that the derivative of a sum of functions is equal to the sum of their derivatives is especially important because the same cannot be said for the product of functions:ĭefinition of ‘power’ from The Concise Oxford Dictionary of Mathematics, 5th ed.We’re differentiating with respect to t, not x.While the former may work well trying to find the derivative of x² + sin( x) (just write down the rule, define f( x) = x² and g( x) = sin( x), and Bob’s your uncle), finding ḟ( t) where f( t) = t² + 3 t⁵+ sin( t) we run into three problems: I don’t know about you, but of those two options I prefer the latter. ‘The derivative of a sum of functions is equal to the sum of their derivatives.’.‘d by d x of … f of x plus g of x … equals d by d x of f of x … plus d by d x of g of x.’.When applying the first rule, I think there are basically two things I could say: Using these basic properties of differentiation becomes second nature, and so you can forget that these things needed to be proved! When I’m creating solution videos for calculus problems as part of my job, I like to make it explicit whenever I use one of these rules. ![]()
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