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Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$
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$\frac{d}{dx}\left(x\right)\ln\left(y\right)+x\frac{d}{dx}\left(\ln\left(y\right)\right)=\frac{d}{dx}\left(y\right)\ln\left(x\right)+y\frac{d}{dx}\left(\ln\left(x\right)\right)$
Learn how to solve implicit differentiation problems step by step online. Find the implicit derivative d/dx(xln(y))=d/dx(yln(x)). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g'. The derivative of the linear function is equal to 1. The derivative of the linear function is equal to 1. The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If f(x)=ln\:a (where a is a function of x), then \displaystyle f'(x)=\frac{a'}{a}.