Differentiating for fun-II

Calculus Level 2

If y = x x y={ x }^{ x } , then d 2 y d x 2 − 1 y ( d y d x ) 2 − y x \frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } -\frac { 1 }{ y } { \left( \frac { dy }{ dx } \right) }^{ 2 }-\frac { y }{ x } is:


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Swapnil Das by Swapnil Das , 20, India

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2 solutions

Raj Rajput
Aug 11, 2015

7 Helpful 0 Interesting 0 Brilliant 0 Confused

Take log of both sides and differentiate w.r.t. x. Some expression of dy/dx comes in terms of x and y. Differentiate that again. Substitute into the expression, after some re-arrangements everything will cancel out.

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