Find the derivatives of the following functions with respect to corresponding independent variables: y = sinx1+cosx - Mathematics

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

y = `sinx/(1 + cosx)`

योग

y = `sinx/(1 + cosx)`

= `u/v` ....(say)

u = sin x v = 1 + cos x

u’ = cos x v’ = – sin x

y = `u/v`

⇒ y' = `(vu"'" - uv"'")/v^2`

(i.e.,) `("d"y)/("d"x) = ((1 + cosx) cosx - sin(0 - sinx))/(1 + cosx)^2`

`("d"y)/("d"x) = (cosx + cos^2 x - sin^2x)/(1 + cosx)^2`

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

= `1/(1 + cosx)`

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Differentiation Rules

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अध्याय 10: Differential Calculus - Differentiability and Methods of Differentiation - Exercise 10.2 [पृष्ठ १६०]

अध्याय 10 Differential Calculus - Differentiability and Methods of Differentiation
Exercise 10.2 | Q 9 | पृष्ठ १६०

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

y = sin x + cos 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 = cosec x . cot x

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

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

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y = (2x – 5)⁴ (8x² – 5)^–3

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y = `x"e"^(-x^2)`

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s(t) = `root(4)(("t"^3 + 1)/("t"^3 - 1)`

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y = tan (cos x)

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y = `5^((-1)/x)`

Differentiate the following:
y = sin³x + cos³x

Differentiate the following:

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

Find the derivatives of the following:
y = `x^(cosx)`