Differentiate the following:y = x+x

Differentiate the following:
y = `sqrt(x +sqrt(x)`

योग

y = `sqrt(x +sqrt(x)`

y = `[x + x^(1/2)]^(1/2)`

y = f(g(x))

`("d"y)/("d"x)` = f'(g(x)) . g'(x)

`("d"y)/("d"x) = 1/2 [x + x^(1/2)]^(1/2 - 1) [1 + 1/2 x^(1/2 - 1)]`

`("d"y)/("d"x) = 1/2[x + x^(1/2)]^(- 1/2) [1 + 1/2 x^(- 1/2)]`

= `1/[2x + x^(1/2)]^(1/2) [1 + 1/(2x^(1/2))]`

= `1/(2sqrt(x + sqrt(x))) xx [(2x^(1/2) + 1)/(2x^(1/2))]`

= `1/(2sqrt(x + sqrt(x))) xx [(2sqrt(x) + 1)/(2sqrt(x))]`

`("d"y)/("d"x) = (2sqrt(x) + 1)/(4sqrt(x) * sqrt(x sqrt(x))`

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अध्याय 10: Differential Calculus - Differentiability and Methods of Differentiation - Exercise 10.3 [पृष्ठ १६४]

अध्याय 10 Differential Calculus - Differentiability and Methods of Differentiation
Exercise 10.3 | Q 26 | पृष्ठ १६४

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

y = e^x sin x

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y = cosec x . cot x

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y = (x² + 5) log(1 + x) e^–3x

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y = cos (tan x)

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

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y = (1 + cos²)⁶

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y = `x^(logx) + (logx)^x`