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Question
Select the correct answer from the given alternative:
If y = `(3x + 5)/(4x + 5)`, then `("d"y)/("d"x)` =
Options
`-15/(3x + 5)^2`
`-15/(4x + 5)^2`
`-5/(4x + 5)^2`
`-13/(4x + 5)^2`
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Solution
`-5/(4x + 5)^2`
Explanation;
y = `(3x + 5)/(4x + 5)`
Differentiating w.r.t. x, we get
`("d"y)/("d"x) = ((4x + 5) "d"/("d"x) (3x + 5) - (3x + 5) "d"/("d"x) (4x + 5))/(4x + 5)^2`
= `(3(4x + 5) - 4(3x + 5))/(4x + 5)^2`
= `- (5)/(4x + 5)^2`
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