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Solution assignment 21 Chain rule

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Assignment 21

Differentiate:

y=e^{\ln(x)}

Solution

Using the informal chain rule yields (the 'quote' means: the derivative of):

y'=e^{\ln(x)}\cdot[\ln(x)]'=\displaystyle\frac{e^{\ln(x)}}{x}

Note that y=e^{\ln(x)}=x and thus this function has the derivative y'=1 as expected.

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