Can someone give me a hint about transforming $\displaystyle x^{4x}$ into a quotient? I think it involves setting y equal to it and taking a log or something.

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- Dec 28th 2013, 11:11 AMpolarbear73Exponential expression
Can someone give me a hint about transforming $\displaystyle x^{4x}$ into a quotient? I think it involves setting y equal to it and taking a log or something.

- Dec 28th 2013, 11:16 AMromsekRe: Exponential expression
can you state the exact problem? What you've written above doesn't make an overwhelming amount of sense.

- Dec 28th 2013, 03:56 PMHallsofIvyRe: Exponential expression
A quotient? What about $\displaystyle \dfrac{1}{x^{-4x}}$?

But I suspect you are really talking about the**derivative**. If we let $\displaystyle y= x^{4x}$ then $\displaystyle ln(y)= ln(x^{4x})= 4x ln(x)$ so that $\displaystyle \frac{1}{y} y'= 4 ln(x)+ \frac{4x}{x}= 4 ln(x)+ 4$ so that $\displaystyle y'= 4y(ln(x)+ 1)= 4x^4(ln(x)+ 1)$. - Dec 29th 2013, 08:49 AMSlipEternalRe: Exponential expression
- Jan 2nd 2014, 05:22 AMHallsofIvyRe: Exponential expression
Yes, thanks.