Find the derivatives of the following: x = tt1-t21+t2, y = tt2t1+t2 - Mathematics

Find the derivatives of the following:

x = `(1 - "t"^2)/(1 + "t"^2)`, y = `(2"t")/(1 + "t"^2)`

बेरीज

x = `(1 - "t"^2)/(1 + "t"^2)`, y = `(2"t")/(1 + "t"^2)`

Put t = tan θ

x = `(1 - tan^2theta)/(1 + tan^2theta)` y = `(2tantheta)/(1 + tan^2theta)`

x = cos 2θ, y = sin 2θ

`("d"x)/("d"theta) = - sin 2theta xx 2`, `("d"y)/("d"theta) = cos 2theta xx 2`

`("d"x)/("d"theta) = - 2 sin 2theta`, `("d"y)/("d"theta) = 2 cos 2theta`

`(("d"y)/("d"theta))/(("d"x)/("d"theta)) = (2 cos 2theta)/(-2 sin 2theta)`

`("d"y)/("d"x) = - cot 2theta`

tan 2θ = `(2tantheta)/(1 - tan^2theta)`

cot 2θ = `(1 - tan^2theta)/(2tantheta)`

= `- (1 - tan^2theta)/(2tantheta)`

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

`("d"y)/("d"x) = ("t"^2 - 1)/(2"t")`

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Differentiation Rules

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पाठ 10: Differential Calculus - Differentiability and Methods of Differentiation - Exercise 10.4 [पृष्ठ १७६]

पाठ 10 Differential Calculus - Differentiability and Methods of Differentiation
Exercise 10.4 | Q 15 | पृष्ठ १७६

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 = tan θ (sin θ + cos θ)

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

Differentiate the following:
y = tan (cos x)

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

Differentiate the following:

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

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

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

Differentiate the following:

y = `sin^-1 ((1 - x^2)/(1 + x^2))`

Find the derivatives of the following:

`x^2/"a"^2 + y^2/"b"^2` = 1

Find the derivatives of the following:

`tan^-1 = ((6x)/(1 - 9x^2))`

Find the derivatives of the following:

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

Find the derivatives of the following:

If y = sin^–1x then find y”