Oh Lawd ... INFINITY !

Calculus Level 2

Note : log = Log base e

y^2 x^2 yx^2 None

Pinkie Pie by Pinkie Pie , 22, India

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3 solutions

Shravan Jain
Mar 21, 2014

y = x y log ⁡ y = y log ⁡ x 1 y d y d x = d y d x log ⁡ x + y x d y d x = y log ⁡ x d y d x + y 2 x ( 1 − y log ⁡ x ) d y d x = y 2 x x ( 1 − y log ⁡ x ) d y d x = y 2 y={ x }^{ y }\\ \log { y=y\log { x } } \\ \frac { 1 }{ y } \frac { dy }{ dx } =\frac { dy }{ dx } \log { x } +\frac { y }{ x } \\ \frac { dy }{ dx } =y\log { x } \frac { dy }{ dx } +\frac { { y }^{ 2 } }{ x } \\ \left( 1-y\log { x } \right) \frac { dy }{ dx } =\frac { { y }^{ 2 } }{ x } \\ x\left( 1-y\log { x } \right) \frac { dy }{ dx } =\quad \boxed { { y }^{ 2 } }

6 Helpful 0 Interesting 0 Brilliant 0 Confused
Pinkie Pie
Mar 19, 2014

Well , have a clue y = x y y=x^y

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Pramit Das
Mar 22, 2014

y=x^y , so , log y =y log x and the rest folllows easily

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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