## Final Answer

## Step-by-step Solution

Problem to solve:

Specify the solving method

Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable

Learn how to solve implicit differentiation problems step by step online.

$\frac{d}{dx}\left(4x^3+7xy^2\right)=\frac{d}{dx}\left(2y^3\right)$

Learn how to solve implicit differentiation problems step by step online. Find the implicit derivative (d/dx)(4x^3+7xy^2=2y^3). 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 (2) is equal to the constant times the derivative of the function. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. The derivative of the linear function is equal to 1.