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Find the derivative of $r^2$ 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 $r^2$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
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$\lim_{h\to0}\left(\frac{\left(r+h\right)^2-r^2}{h}\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of r^2 using the definition. Find the derivative of r^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 r^2. Substituting f(x+h) and f(x) on the limit, we get. Expand \left(r+h\right)^2. Cancel like terms r^2 and -r^2. Factor the polynomial 2rh+h^2 by it's greatest common factor (GCF): h.