use the definition of the derivative to evaluate v=4/2pir^3
"f'(x)=\\displaystyle{\\lim_{h\\to 0}}\\frac{f(x+h)-f(x)}{h}"
"\\frac{dv}{dr}=\\frac{4\\pi}{2}\\displaystyle{\\lim_{h\\to 0}}\\frac{v(r+h)-f(r)}{h}=2\\pi \\displaystyle{\\lim_{h\\to 0}}\\frac{(r+h)^3-r^3}{h}="
"=2\\pi \\displaystyle{\\lim_{h\\to 0}}\\frac{r^3+3r^2h+3rh^2+h^3-r^3}{h}=2\\pi \\displaystyle{\\lim_{h\\to 0}}(3r^2+3rh+h^2)="
"=2\\pi\\cdot 3r^2=6\\pi r^2"
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