Differentiate the following:y = sin2(cos kx)

Differentiate the following:
y = sin²(cos kx)

Sum

y = sin²(cos kx)

y = f(g(x)

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

`("d"y)/("d"x)` = 2 sin(cos kx) × cos(cos kx) × – sin kx × k × 1

`("d"y)/("d"x)` = sin(2 cos kx) × – k sin kx

`("d"y)/("d"x)` = – k sin kx . sin(2 cos kx)

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Differentiation Rules

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Chapter 10: Differential Calculus - Differentiability and Methods of Differentiation - Exercise 10.3 [Page 164]

Chapter 10 Differential Calculus - Differentiability and Methods of Differentiation
Exercise 10.3 | Q 23 | Page 164

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 = `tan x/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 = (x² + 5) log(1 + x) e^–3x

Differentiate the following:
y = tan 3x

Differentiate the following:
y = sin (e^x)

Differentiate the following:

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

Differentiate the following:
y = tan (cos x)

Differentiate the following:
y = sin³x + cos³x

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

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

Find the derivatives of the following:

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

Find the derivatives of the following:

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

Find the derivatives of the following:

`tan^-1 = ((6x)/(1 - 9x^2))`