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Question
Differentiate the following:
f(x) = `x/sqrt(7 - 3x)`
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Solution
f(x) = `x/sqrt(7 - 3x)`
= `x/(7 - 3x)^(1/2)`
f'(x) = `((7 - 3x)^(1/2) xx 1 - x xx 1/2 (7 - 3x)^(1/2 - 1) (- 3))/[(7 - 3x)^(1/2)]^2`
= `((7 - 3x)^(1/2) + 3/2 xx (7 - 3x)^(- 1/2))/((7 - 3x))`
= `((7 - 3)^(1/2) + (3x)/(2(7 - 3x)^(1/2)))/((7 - 3x))`
= `(((7 - 3x)^(1/2) xx 2(7 - 3x)^(1/2) + 3x)/(2(7 - 3x)^(1/2)))/((7 - 3x))`
= `(2(7 - 3x) + 3x)/(2(7 - 3x)^(1/2) (7 - 3x))`
= `(14 - 6x + 3x)/(2(7 - 3x)^(3/2)`
f'(x) = `(14 - 3x)/(2(7 - 3x)^(3/2)`
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