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Find the derivative of $\frac{-x}{y}$ 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 $\frac{-x}{y}$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
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$\lim_{h\to0}\left(\frac{\frac{-\left(x+h\right)}{y}-\frac{-x}{y}}{h}\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of (-x)/y using the definition. Find the derivative of \frac{-x}{y} 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{-x}{y}. Substituting f(x+h) and f(x) on the limit, we get. Multiplying the fraction by -1. Simplify the product -(x+h). The least common multiple (LCM) of a sum of algebraic fractions consists of the product of the common factors with the greatest exponent, and the uncommon factors.