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What is differentiation and how do I do it?

explain the following briefly: To work out the gradient, first principles, shortcutsexplain in detail: different methods

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I can differentiate exponentials (e^x), but how can I differentiate ln(x)?

Find X log(x)=4 Base 10

Differentiate 2x/cos(x)

By integrating, find the area between the curve and x axis of y = x*exp(x) between x = 0 and x = 1

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