Differentiate the following:y = x+x - Mathematics

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

बेरीज

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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Differentiation Rules

या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?

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

पाठ 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

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

y = sin x⁰

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

y = log₁₀ x

Differentiate the following:
y = tan 3x

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

Differentiate the following:
y = cos (a³ + x³)

Differentiate the following:

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

Differentiate the following:
y = `"e"^(xcosx)`

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

Find the derivatives of the following:

(cos x)^{log x}