Question
For some constants a and b, find the derivative of$\frac{\text{x}-\text{a}}{\text{x}-\text{b}}$
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Answer
$\Rightarrow\text{f}'(\text{x})=\frac{\text{d}}{\text{dx}}\bigg(\frac{\text{x}-\text{a}}{\text{x}-\text{b}}\bigg)$ By quotient rule, $\text{f}'(\text{x})=\frac{(\text{x}-\text{b})\frac{\text{d}}{\text{dx}}(\text{x}-\text{a})-(\text{x}-\text{a})\frac{\text{d}}{\text{dx}}(\text{x}-\text{b})}{(\text{x}-\text{b})^2}$ $=\frac{\text{x}-\text{b}-\text{x}+\text{a}}{(\text{x}-\text{b})^2}$$=\frac{\text{a}-\text{b}}{(\text{x}-\text{b})^2}$
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