Friday

December 19, 2014

December 19, 2014

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

**Answer this Question**

**Related Questions**

applied calculus - 1. Consider the function y = xx (for x> 0). a) Why does ...

math - I have the same project as Jill down there... -What is the definition of ...

Calc - I'm creating a "calculu for dummies" project book. I've already done most...

Applied Calculus - Find the first and second derivative of the function: x/(7x+...

Calculus - Explain the global optimization process for a continuous function ...

Calculus - Explain the global optimization process for a continuous function ...

Math, Calculus - Find the derivative of the function. y= xcosx - sinx What's the...

Calculus (Global Max) - Explain the global optimization process for a continuous...

math - can some one please help me with the following questions as i dont ...

Applied Calculus - Find the derivative of this function: g(t)=(8t+10)^2*(10t^2-7...