Find the implicit derivative $\frac{d}{dx}\left(4x\sqrt[3]{y}-\ln\left(4x^3+y^4\right)-\sqrt{x+1}-e^{2y}\right)=0$

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$\frac{d}{dx}\left(4x\sqrt[3]{y}\right)+\frac{d}{dx}\left(-\ln\left(4x^3+y^4\right)\right)+\frac{d}{dx}\left(-\sqrt{x+1}\right)+\frac{d}{dx}\left(-e^{2y}\right)=0$

Learn how to solve implicit differentiation problems step by step online. Find the implicit derivative d/dx(4xy^(1/3)-ln(4x^3+y^4)-(x+1)^(1/2)-e^(2y))=0. The derivative of a sum of two or more functions is the sum of the derivatives of each function. 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=\sqrt[3]{y}. The derivative of the linear function is equal to 1.