Find dy/dx using logarithmic differentiation y=[(x+1)(x+2)]/[(x-1)(x-2)]?

Y^(3x)=(tan^1 x^2)^(1/3) (x+3^x)^-2 ----------------(1)==> y = (tan^1 x^2)^(1/3) (x+3^x)^-2 ^(1/3x) let 3^x = t take logs x ln(3) = ln(t) differentiating with respect to x ln(3) = (1/t) dt/dx dt/dx = t ln(3) dt/dx = ln(3) 3^x-----------(2) now eqn (1) becomes y^(3x) = { tan^-1(x^2) }^(1/3) (x + t)^(-2) take logs 3x ln(y) = (1/3) ln tan^-1(x^2) - 2 ln (x + t) ==> ln(y) = ln tan^-1(x^2) - 6 ln (x + t) /9x differentiate with respect to x.

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