Final answer to the problem
$y^{\prime}=\frac{-1-x^2y^2+xy+y^2}{1+x^2y^2-x^2-yx}$
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Step-by-step Solution
Learn how to solve differential equations problems step by step online. Find the implicit derivative d/dx(ln(x+y)=arctan(xy)). Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If f(x)=ln\:a (where a is a function of x), then \displaystyle f'(x)=\frac{a'}{a}. The derivative of a sum of two or more functions is the sum of the derivatives of each function. Taking the derivative of arctangent.
Final answer to the problem
$y^{\prime}=\frac{-1-x^2y^2+xy+y^2}{1+x^2y^2-x^2-yx}$
