Differentiate the following: y = (x2+1)x2+23

Differentiate the following:

y = `(x^2 + 1) root(3)(x^2 + 2)`

बेरीज

y = `(x^2 + 1) root(3)(x^2 + 2)`

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

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

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

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

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

= `(2x^3 + 2x + 6x (x^2 + 2)^(1/3 + 2/3))/(3(x^2 + 2)^(2/3)`

= `(2x^2 + 2x + 6x(x^2 + 2))/(3(x^2 + 2)^(2/3)`

= `(2x^3 + 2x + 6x^3 + 12x)/(3(x^2 + 2)^(2/3)`

`("d"y)/("d"x) = (8x^3 + 14x)/(3(x^2 + 2)^(2/3)`

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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 १६३]

पाठ 10 Differential Calculus - Differentiability and Methods of Differentiation
Exercise 10.3 | Q 14 | पृष्ठ १६३

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 = log₁₀ x

Differentiate the following:

h(t) = `("t" - 1/"t")^(3/2)`

Differentiate the following:

y = `(sin^2x)/cos x`

Differentiate the following:
y = `sqrt(1 + 2tanx)`

Differentiate the following:
y = sin²(cos kx)

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