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HillDP
y^2=2a^3x/x^2+a^2 implicit differentiation
i didnt get the right answer. ive tried to solve it.
thats the right equation, help me get the answer. thanks.
d/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^2-x (2 x)))/(a^2+x^2)^2