Question

Simple calculus question?

Answer 1

25 and 3 ducks plus 1 pigeon

Answer 2

\[y=\ln \left( e ^{2x}+x ^{2} -2x\right)\]
Can somebody explain to me how do I make the semplification in order to get this expression?
\[y=2x+\ln (1+\frac{ x ^{2}-2x}{ e ^{2x} })\]

Answer 3

I was writing it just now...

Answer 4

English is not my first language so sorry if I make some mistakes.

Answer 5

They factored out e^(2x). Then they used the rules

ln(xy) = ln(x) + ln(y)
ln(x^y) = y*ln(x)
ln(e) = 1

Doing all that gives you this:

\[\large y=\ln \left( e ^{2x}+x ^{2} -2x\right)\]
\[\large y=\ln \left( e ^{2x}(1+\frac{x ^{2} -2x}{e^{2x}})\right)\]
\[\large y=\ln \left( e ^{2x}\right) + \ln\left(1+\frac{x ^{2} -2x}{e^{2x}}\right)\]
\[\large y=2x*\ln \left( e\right) + \ln\left(1+\frac{x ^{2} -2x}{e^{2x}}\right)\]
\[\large y=2x*1 + \ln\left(1+\frac{x ^{2} -2x}{e^{2x}}\right)\]
\[\large y=2x + \ln\left(1+\frac{x ^{2} -2x}{e^{2x}}\right)\]

Answer 6

@jim_thompson5910 excuse me, I got a question how do you write like that? with all those letters and the equations so perfect lol

Answer 7

you can use the equation button below the text input box to enter equations

I'm using Tex to render the formulas

http://en.wikipedia.org/wiki/TeX

so for instance, to render \(\Large y = x^{3t}\) you would type

y = x^{3t}

and surround that with "\ [" and "\ ]" , ie

\ [ y = x^{3t} \ ]

delete all the spaces to make it render

Answer 8

\[y=x^{3t}\]

Answer 9

ohh lol okay thanks it will take me a long time to get adapted to this but thanks :D @jim_thompson5910