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Differentiate the following: f(x) = x7-3x - Mathematics

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प्रश्न

Differentiate the following:

f(x) = `x/sqrt(7 - 3x)`

बेरीज
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उत्तर

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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Differentiation Rules
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 10: Differential Calculus - Differentiability and Methods of Differentiation - Exercise 10.3 [पृष्ठ १६३]

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सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 11 TN Board
पाठ 10 Differential Calculus - Differentiability and Methods of Differentiation
Exercise 10.3 | Q 17 | पृष्ठ १६३

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