Differentiate the following:y = sin(tan(sinx)) - Mathematics

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

योग

y = `sin(tan(sqrt(sinx)))`

y = f(g(x))

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

`("d"y)/("d"x) = cos(tan(sqrt(sinx))) sec^2(sqrt(sinx)) xx 1/2(sinx)^(1/2 - 1) cos x`

`("d"y)/("d"x) = 1/2 cos (tan(sqrt(sinx))) sec^2 (sqrt(sinx)) (sinx)^(- 1/2) cosx`

`("d"y)/("d"x) = (cos(tan(sqrt(sinx))) sec^2(sqrt(sinx)) cosx)/(2(sinx)^(1/2)`

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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 29 | पृष्ठ १६४

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

f(x) = x – 3 sin x

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

g(t) = 4 sec t + tan t

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

y = log₁₀ x

Differentiate the following:
F(x) = (x³ + 4x)⁷

Differentiate the following:

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

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

Find the derivatives of the following:

(cos x)^{log x}