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January 24, 2015

January 24, 2015

Posted by **jack** on Monday, April 8, 2013 at 5:31pm.

a) Why does the derivative rule for xn not apply?

b) Why does the derivative rule for ax not apply?

c) What are the four magic properties of logarithms?

d) Take the ln of both sides. Use the properties of logarithms and implicit differentiation to determine y. Express your answer as a function of x only.

- Applied calculas -
**Reiny**, Monday, April 8, 2013 at 6:34pmYou must mean y = x^x or y = x

^{x}

take ln of both sides

ln y = ln (x^x)

ln y = x lnx

now differentiate:

y'/y = x(1/x) + (1)lnx = 1 + lnx

y' = y(1 + lnx) = y + lnx

or

y' = x^x + lnx

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