Differentiate the following:y = tan (cos x) - Mathematics

Differentiate the following:
y = tan (cos x)

Sum

y = tan (cos x)

[y = f(g(x)

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

`("d"y)/("d"x) = sec^2(cos x) xx "d"/("d"x) (cos x)`

= sec² (cos x) × – sin x

`("d"y)/("d"x)` = – sin x . sec²(cos x)

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Chapter 10: Differential Calculus - Differentiability and Methods of Differentiation - Exercise 10.3 [Page 163]

Chapter 10 Differential Calculus - Differentiability and Methods of Differentiation
Exercise 10.3 | Q 18 | Page 163

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:

y = cos x – 2 tan x

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

y = e^x sin x

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

y = `sinx/x^2`

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

y = (x² + 5) log(1 + x) e^–3x

Differentiate the following:
y = cos (tan x)

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

Differentiate the following:

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

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

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:

(cos x)^{log x}

Find the derivatives of the following:

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

Find the derivatives of the following:

Find the derivative of sin x² with respect to x²

Find the derivatives of the following:

If x = a(θ + sin θ), y = a(1 – cos θ) then prove that at θ = `pi/2`, yⁿ = `1/"a"`