Differentiate the following function with respect to x: (ax+b) (c… - Vidyadip

Question

Differentiate the following function with respect to x:

$\frac{(\text{ax}+\text{b})}{(\text{cx}+\text{d})}$

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Answer

$\frac{\text{d}}{\text{dx}}\Big(\frac{\text{ax}+\text{b}}{\text{cx}+\text{d}}\Big)=\frac{(\text{cx}+\text{d})\frac{\text{d}}{\text{dx}}(\text{ax}+\text{b})-(\text{ax}+\text{b})\frac{\text{d}}{\text{dx}}(\text{cx}+\text{d})}{(\text{cx}+\text{d})^2}$ (Using divident rule)

$=\frac{(\text{cx}+\text{d})\text{a}-(\text{ax}+\text{b})\text{c}}{(\text{cx}+\text{d})^2}$

$=\frac{(\text{axc}+\text{ad}-\text{axc}-\text{bc})}{(\text{cx}+\text{d})^2}$

$=\frac{\text{ad}-\text{bc}}{(\text{cx}+\text{d})^2}$

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