Solving: $\frac{d}{dx}\left(3y^2x=y+\cos\left(x\right)\right)$
Exercise
$\frac{dy}{dx}\left(3y^2x=y+cosx\right)$
Step-by-step Solution
Learn how to solve problems step by step online. Find the implicit derivative d/dx(3y^2x=y+cos(x)). 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=y^2 and g=x. The derivative of the linear function is equal to 1.
Find the implicit derivative d/dx(3y^2x=y+cos(x))
Final answer to the exercise
$y^{\prime}=\frac{-\sin\left(x\right)-3y^2}{6yx-1}$