Is there a difference between x^x and, say, 10^x when differentiating?
When I differentiate x^x I get x^x(lnx+1) but when I differentiate 10^x I seem to get 10^x(log10)
How is a number^x differentiated? I understand the x^x part.
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Now let , then and , so .
As for , first note that it is only continuous, and so only differentiable, when , then
Equivalently, if then . Differentiating, so that .
Similarly, if then . Differentiating (using the product rule on the right), so that .
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