Check Your Understanding Is the equation
One further point thin needs to be mentioned is the effect of the operations of calculus on dimensions. We have seen that dimensions obey the rules of algebra, just like units, but what happens when we take the derivative of one physical quantity with respect to another or integrate a physical quantity over another? The derivative of a function is just the slope of the line tangent to its graph and slopes are ratios, so for physical quantities
Similarly, since integrals are just sums of products, the dimension of the integral of
By the same reasoning, analogous rules hold for the units of physical quantities derived from other quantities by integration or differentiation.
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