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

Differentiate the following:

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

बेरीज

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

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पाठ 10: Differential Calculus - Differentiability and Methods of Differentiation - Exercise 10.3 [पृष्ठ १६३]

पाठ 10 Differential Calculus - Differentiability and Methods of Differentiation
Exercise 10.3 | Q 17 | पृष्ठ १६३

Find the derivatives of the following functions with respect to corresponding independent variables:

y = cos x – 2 tan x

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y = (x² + 4x + 6)⁵

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y = 4 sec 5x

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y = `sqrt(1 + 2tanx)`

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y = sin²(cos kx)

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y = `"e"^(xcosx)`

Find the derivatives of the following:
`sqrt(x) = "e"^((x - y))`

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(cos x)^{log x}

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`x^2/"a"^2 + y^2/"b"^2` = 1

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`sqrt(x^2 + y^2) = tan^-1 (y/x)`

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Find the derivative with `tan^-1 ((sinx)/(1 + cos x))` with respect to `tan^-1 ((cosx)/(1 + sinx))`

Find the derivatives of the following:

If y = sin^–1x then find y”

Find the derivatives of the following:

If y = `(cos^-1 x)^2`, prove that `(1 - x^2) ("d"^2y)/("d"x)^2 - x ("d"y)/("d"x) - 2` = 0. Hence find y₂ when x = 0