Find the implicit derivative $\frac{d}{dx}\left(\ln\left(y\right)=4x\ln\left(x\right)\right)$

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Learn how to solve product rule of differentiation problems step by step online. Find the implicit derivative d/dx(ln(y)=4xln(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=x and g=\ln\left(x\right). The derivative of the linear function is equal to 1.