Differentiate the following: y = sin-1(1-x21+x2)

Differentiate the following:

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

Sum

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

y = f(g(x)

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

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

= `1/sqrt(((1 + x^2)^2 - (1 - x^2)^2)/(1 + x^2)^2) xx ((1 + x^2)(- 2x) - (1 - x^2)(2x))/(1 + x^2)^2`

= `1/sqrt((1 + 2x^2 + x^4 - (1 - 2x^2 + x^4))/((1 + x^2))) xx (-2x - 2x^3 - 2x + 2x^3)/(1 + x^2)^2`

= `(1 + x^2)/sqrt(1 + 2x^2 + x^4 - 1 + 2x^2 - x^4) xx (-4x)/(1 + x^2)^2`

= `(-4x)/(sqrt(4x^2) (1 + x^2))`

`("d"y)/("d"x) = (-4x)/(2x(1 + x^2))`

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

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Differentiation Rules

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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 30 | Page 164

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

g(t) = t³ cos t

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

y = log₁₀ x

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

Differentiate the following:
y = e^–mx

Differentiate the following:

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

Differentiate the following:
y = (1 + cos²)⁶

Differentiate the following:

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

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

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

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

Differentiate the following:
y = `sin(tan(sqrt(sinx)))`