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The derivative of a sum of two or more functions is the sum of the derivatives of each function
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$\frac{d}{dx}\left(xy^2\right)+\frac{d}{dx}\left(-x^2\right)+\frac{d}{dx}\left(4\right)=0$
Learn how to solve implicit differentiation problems step by step online. Find the implicit derivative d/dx(xy^2-x^2+4)=0. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of the constant function (4) is equal to zero. The derivative of a function multiplied by a constant (-1) is equal to the constant times the derivative of the function. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x and g=y^2.