Find the implicit derivative $\frac{d}{dx}\left(\sqrt[3]{a+x^2}+\sqrt[3]{b+y^2}=\sqrt[3]{cx}\right)$

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$\frac{d}{dx}\left(\sqrt[3]{a+x^2}+\sqrt[3]{b+y^2}\right)=\frac{d}{dx}\left(\sqrt[3]{cx}\right)$

Learn how to solve problems step by step online. Find the implicit derivative d/dx((a+x^2)^1/3+(b+y^2)^1/3=(cx)^1/3). Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. 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 a function multiplied by a constant is equal to the constant times the derivative of the function. The derivative of the linear function is equal to 1.