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Combining like terms $\frac{1}{3}xy$ and $\frac{1}{2}xy$
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$derivdef\left(\frac{1}{2}x^2+\frac{5}{6}xy+\frac{1}{4}y^2\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of 1/2x^2+1/3xy1/2xy1/4y^2 using the definition. Combining like terms \frac{1}{3}xy and \frac{1}{2}xy. Find the derivative of \frac{1}{2}x^2+\frac{5}{6}xy+\frac{1}{4}y^2 using the definition. Apply the definition of the derivative: \displaystyle f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}. The function f(x) is the function we want to differentiate, which is \frac{1}{2}x^2+\frac{5}{6}xy+\frac{1}{4}y^2. Substituting f(x+h) and f(x) on the limit, we get. Multiply the single term -1 by each term of the polynomial \left(\frac{1}{2}x^2+\frac{5}{6}xy+\frac{1}{4}y^2\right). Simplifying.