Solving: $\frac{d}{dx}\left(x^3+y^3=3xy\right)$
Exercise
$\frac{dy}{dx}\left(x^3\:+\:y^3\:=\:3xy\:\right)$
Step-by-step Solution
Learn how to solve limits by direct substitution problems step by step online. Find the implicit derivative d/dx(x^3+y^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^3+y^3=3xy)
Final answer to the exercise
$y^{\prime}=\frac{-x^{2}-y^{\left(2+{\prime}\right)}+y}{-x}$