Final answer to the problem
$\frac{1}{1+x^{4}y^2}x\left(2y+xy^{\prime}\right)=x+xy^2$
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Step-by-step Solution
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Taking the derivative of arctangent
$\frac{1}{1+\left(x^2y\right)^2}\frac{d}{dx}\left(x^2y\right)=x+xy^2$
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$\frac{1}{1+\left(x^2y\right)^2}\frac{d}{dx}\left(x^2y\right)=x+xy^2$
Learn how to solve problems step by step online. Find the implicit derivative d/dx(arctan(x^2y))=x+xy^2. Taking the derivative of arctangent. The power of a product is equal to the product of it's factors raised to the same power. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=. The derivative of the linear function is equal to 1.
Final answer to the problem
$\frac{1}{1+x^{4}y^2}x\left(2y+xy^{\prime}\right)=x+xy^2$