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

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$\frac{1}{xy}\frac{d}{dx}\left(xy\right)=e^{\frac{x}{y}}$

Learn how to solve implicit differentiation problems step by step online. Find the implicit derivative d/dx(ln(xy))=e^(x/y). 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}. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x and g=y. The derivative of the linear function is equal to 1. The derivative of the linear function is equal to 1.