Final answer to the problem
$2e^xy+\frac{1}{y}$
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Step-by-step Solution
Learn how to solve sum rule of differentiation problems step by step online. Find the derivative d/dy(y^2e^x+ln(xy)) using the sum rule. 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. 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 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}.
Final answer to the problem
$2e^xy+\frac{1}{y}$
