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Question
Differentiate the following w.r.t.x: `x/(sqrt(7 - 3x)`
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Solution
Let y = `x/(sqrt(7 - 3x)`
Differentiating w.r.t. x, we get
`"dy"/"dx" = "d"/"dx"(x/sqrt(7 - 3x))`
= `(sqrt(7 - 3x)."d"/"dx"(x) - x"d"/"dx"(sqrt(7 - 3x)))/((sqrt(7 - 3x))^2`
= `(sqrt(7 - 3x) xx 1 - x xx (1)/(2sqrt(7 - 3x))."d"/"dx"(7 - 3x))/(7 - 3x)`
`= (sqrt(7 - 3x) - x/(2sqrt(7 - 3x))(0 - 3 xx 1))/(7 - 3x)`
`= (2(7 - 3x) + 3x)/(2(7 - 3x)^(3/2)`
`= (14 - 6x + 3x)/(2(7 - 3x)^(3/2)`
= `(14 - 3x)/(2(7 - 3x)^(3/2)`.
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