Differentiate the following:y = x+x

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

Sum

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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Chapter 10: Differential Calculus - Differentiability and Methods of Differentiation - Exercise 10.3 [Page 164]

Chapter 10 Differential Calculus - Differentiability and Methods of Differentiation
Exercise 10.3 | Q 26 | Page 164

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

y = `tan x/x`

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

y = `x/(sin x + cosx)`

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

y = `(tanx - 1)/secx`

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

y = `sinx/x^2`

Differentiate the following:
y = (x² + 4x + 6)⁵

Differentiate the following:
y = cos (tan x)

Differentiate the following:
y = `root(3)(1 + x^3)`

Differentiate the following:
y = e^–mx

Differentiate the following:
y = 4 sec 5x

Differentiate the following:

y = `"e"^(3x)/(1 + "e"^x`

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

Find the derivatives of the following:
x^y = y^x