Differentiate the following:y = 1+x33

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

योग

y = `root(3)(1 + x^3)`

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

[y = f(g(x)

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

`("d"y)/("d"x) = 1/3 (1 + x^3)^(1/3 - 1) xx "d"/("d"x) (1 + x^3)`

`("d"y)/("d"x) = 1/3 (1 + x^3)^(- 2/3) (0 + 3x^2)`

`("d"y)/("d"x) = 1/3 1/(1 + x^3)^(2/3) xx 3x^2`

`("d"y)/("d"x) = x^2/(1 + x^3)^(2/3)`

= `x^2 (1 + x^3)^(- 2/3)`

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

अध्याय 10 Differential Calculus - Differentiability and Methods of Differentiation
Exercise 10.3 | Q 4 | पृष्ठ १६३

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

f(x) = x – 3 sin x

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 = `sinx/(1 + cosx)`

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

y = `(tanx - 1)/secx`

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F(x) = (x³ + 4x)⁷

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y = (2x – 5)⁴ (8x² – 5)^–3

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y = sin²(cos kx)

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

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y = `"e"^(xcosx)`

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`tan^-1sqrt((1 - cos x)/(1 + cos x)`

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If y = sin^–1x then find y”

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Find the derivatives of the following:

If x = a(θ + sin θ), y = a(1 – cos θ) then prove that at θ = `pi/2`, yⁿ = `1/"a"`