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 = `x/(sin x + cosx)`

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

y = tan θ (sin θ + cos θ)

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

y = log₁₀ x

Differentiate the following:

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

Differentiate the following:

f(t) = `root(3)(1 + tan "t")`

Differentiate the following:
y = 4 sec 5x

Differentiate the following:
y = tan (cos x)

Differentiate the following:
y = `sqrt(1 + 2tanx)`

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