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So far, we have the following. (x) - 160 (xy) + d (y) = (16) The derivatives (x2) and (16) can be found using
So far, we have the following. (x) - 160 (xy) + d (y) = (16) The derivatives (x2) and (16) can be found using basic derivative rules learned in previous sections. Doing so gives the following result. d dx d (x) = dx d (16) = dx d However, we note that the derivatives (xy) and (y) involve y. Recall that the derivative of any term involving y will require the chain rule and include the factor dy We also note tha dx the first of these two derivatives involving y is the product of two differentiable functions, so the product rule will be used. Finding each of these derivatives gives the following result. d dx dy -(xy) = X- dx + dx (y) = dy dx
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