How do you use the quotient rule to find the derivative of $y = \frac{a x + b}{c x + d}$ $y=(ax+b)/(cx+d)$ ?

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How do you use the quotient rule to find the derivative of $y = \frac{a x + b}{c x + d}$ $y=(ax+b)/(cx+d)$ ?

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Answer 1 · 2014-07-29T01:28:27

$y'=(ad-bc)/(cx+d)^2$

Using Quotient Rule,

$y=f(x)/g(x)$ , then $y'=(f'(x)g(x)−f(x)g'(x))/(g(x))^2$

$y=(ax+b)/(cx+d)$

differentiating both sides with respect to x,

$y'=((ax+b)'(cx+d)-(ax+b)(cx+d)')/(cx+d)^2$

$y'=(a(cx+d)-(ax+b)c)/(cx+d)^2$

$y'=(ad-bc)/(cx+d)^2$

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How do you use the quotient rule to find the derivative of $y = \frac{a x + b}{c x + d}$ $y=(ax+b)/(cx+d)$ ?

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How do you use the quotient rule to find the derivative of $y = \frac{a x + b}{c x + d}$ $y=(ax+b)/(cx+d)$ ?