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

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

Sum

y = cos (a³ + x³)

[y = f(g(x)

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

`("d"y)/("d"x) = - sin ("a"^3 + x^3) "d"/("d"x) ("a"^3 + x^3)`

`("d"y)/("d"x)` = – sin (a³ + x³)(0 + 3x²)

`("d"y)/("d"x)` = – 3x² sin (a³ + x³)

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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 10 | Page 163

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 = `(tanx - 1)/secx`

Differentiate the following:
y = cos (tan x)

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

Differentiate the following:
y = e^–mx

Differentiate the following:

f(x) = `x/sqrt(7 - 3x)`

Differentiate the following:

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

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

Find the derivatives of the following:
`sqrt(x) = "e"^((x - y))`

Find the derivatives of the following:

(cos x)^{log x}

Find the derivatives of the following:

`x^2/"a"^2 + y^2/"b"^2` = 1

Find the derivatives of the following:

`tan^-1sqrt((1 - cos x)/(1 + cos x)`

Find the derivatives of the following:

sin^-1 (3x – 4x³)

Find the derivatives of the following:

If y = sin^–1x then find y”

Find the derivatives of the following:

If y = `(cos^-1 x)^2`, prove that `(1 - x^2) ("d"^2y)/("d"x)^2 - x ("d"y)/("d"x) - 2` = 0. Hence find y₂ when x = 0