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anonymous
 4 years ago
y^2=2a^3x/x^2+a^2 implicit differentiation
anonymous
 4 years ago
y^2=2a^3x/x^2+a^2 implicit differentiation

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0i didnt get the right answer. ive tried to solve it.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0dw:1342330174045:dw

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0thats the right equation, help me get the answer. thanks.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0d/dx(y^2) = d/dx((2 a^3 x)/(a^2+x^2)) The derivative of y^2 is zero: = 0 = d/dx((2 a^3 x)/(a^2+x^2)) Factor out constants: = 0 = 2 (d/dx((a^3 x)/(a^2+x^2))) Factor out constants: = 0 = 2 (a^3 (d/dx(x/(a^2+x^2)))) Use the quotient rule, d/dx(u/v) = (v ( du)/( dx)u ( dv)/( dx))/v^2, where u = x and v = a^2+x^2: = 0 = 2 a^3 ((a^2+x^2) (d/dx(x))x (d/dx(a^2+x^2)))/(a^2+x^2)^2 The derivative of x is 1: = 0 = (2 a^3 (x (d/dx(a^2+x^2))+a^2+x^2))/(a^2+x^2)^2 Differentiate the sum term by term: = 0 = (2 a^3 (x (d/dx(a^2)+d/dx(x^2))+a^2+x^2))/(a^2+x^2)^2 The derivative of a^2 is zero: = 0 = (2 a^3 (x (d/dx(x^2)+0)+a^2+x^2))/(a^2+x^2)^2 The derivative of x^2 is 2 x: = 0 = (2 a^3 (a^2+x^2x (2 x)))/(a^2+x^2)^2
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