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Differentiate the following w.r.t.x: x7-3x - Mathematics and Statistics

Sum

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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