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** Step-by-step Solution **

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

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

Learn how to solve 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.

** Final Answer

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