Exercise
$\frac{d}{dx}x^2y+xy^3=-3xy$
Step-by-step Solution
Learn how to solve problems step by step online. Find the implicit derivative d/dx(x^2y+xy^3=-3xy). Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. The derivative of a function multiplied by a constant 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. The derivative of the linear function is equal to 1.
Find the implicit derivative d/dx(x^2y+xy^3=-3xy)
Final answer to the exercise
$y^{\prime}=\frac{-2xy-y^3-3xy^{\left(2+{\prime}\right)}-3y}{\left(x+3\right)x}$