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

Differentiate the following:

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

योग

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

अध्याय 10 Differential Calculus - Differentiability and Methods of Differentiation
Exercise 10.3 | Q 30 | पृष्ठ १६४

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

f(x) = x sin x

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g(t) = 4 sec t + tan t

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

y = x sin x cos x

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y = tan 3x

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

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y = `sqrt(1 + 2tanx)`

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y = (1 + cos²)⁶

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

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(cos x)^{log x}

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x = `"a" cos^3"t"` ; y = `"a" sin^3"t"`

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Find the derivative of sin x² with respect to x²

Find the derivatives of the following:

If y = sin^–1x then find y”