SOLUTION: Find dy/dX of the following. a) y=-1/6(e^(-3x))+x^(2x-1) b) 3x^(2)y-xy^(2)=sin^(2)3x

Algebra ->  Circles -> SOLUTION: Find dy/dX of the following. a) y=-1/6(e^(-3x))+x^(2x-1) b) 3x^(2)y-xy^(2)=sin^(2)3x      Log On


   

Question 1067397: Find dy/dX of the following.
a) y=-1/6(e^(-3x))+x^(2x-1)
b) 3x^(2)y-xy^(2)=sin^(2)3x
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find dy/dX of the following.
a) y=-1/6(e^(-3x))+x^(2x-1)
I did that yesterday.
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I'll use CAPS for the variables.
b) 3X^2Y-XY^2 = sin^2(3X)
6XYdx + 3X^2dy -Y^2dx - 2XYdy = 2sin(3X)cos(3X)*3dx
6XYdx - 6sin(3X)cos(3X)dx - Y^2dx = 2XYdy - 3X^2dy
(6XY - 6sin(3X)cos(3X) - Y^2)dx = (2XY - 3X^2)dy
dy/dx = %286XY+-+6sin%283X%29cos%283X%29+-+Y%5E2%29%2F%282XY+-+3X%5E2%29
Or,
dy/dx = %286XY+-+3sin%286X%29+-+Y%5E2%29%2F%282XY+-+3X%5E2%29