Final answer to the problem
$y^{\prime}=\frac{2xy^2+2}{\sec\left(y\right)^2-2x^2y}$
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Step-by-step Solution
Learn how to solve problems step by step online. Find the implicit derivative d/dx(tan(y)=x^2y^2+2x). Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. The derivative of the tangent of a function is equal to secant squared of that function times the derivative of that function, in other words, if {f(x) = tan(x)}, then {f'(x) = sec^2(x)\cdot D_x(x)}. The derivative of the linear function is equal to 1. The derivative of a sum of two or more functions is the sum of the derivatives of each function.
Final answer to the problem
$y^{\prime}=\frac{2xy^2+2}{\sec\left(y\right)^2-2x^2y}$
