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Find the derivative of $-\frac{9}{10}x$ 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 $-\frac{9}{10}x$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
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$\lim_{h\to0}\left(\frac{-\frac{9}{10}\left(x+h\right)+\frac{9}{10}x}{h}\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of (3x)/5-1(3x)/2+-5=-9/10x using the definition. Find the derivative of -\frac{9}{10}x 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{9}{10}x. Substituting f(x+h) and f(x) on the limit, we get. Multiply the single term -\frac{9}{10} by each term of the polynomial \left(x+h\right). Simplifying. Simplify the fraction \frac{-\frac{9}{10}h}{h} by h.