Differentiate the following:y = sin3x + cos3x - Mathematics

Differentiate the following:
y = sin³x + cos³x

बेरीज

y = sin³x + cos³x

Here u = sin³x = (sin x)³

⇒ `("d"u)/("d"x)` = 3(sin x)²(cos x)

= 3sin²x cosx

v = cos³x = (cos x)³

⇒ `("d"u)/("d"x)` = 3(cos x)² (– sin x)

= – 3 sin x cos²x

Now y = u + v

⇒ `("d"y)/("d"x) = ("d"u)/("d"x) + ("d"v)/("d"x)`

= 3 sin²x cos x – 3sin x cos²x

= 3 sin x cos x (sin x – cos x)

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Differentiation Rules

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पाठ 10: Differential Calculus - Differentiability and Methods of Differentiation - Exercise 10.3 [पृष्ठ १६४]

पाठ 10 Differential Calculus - Differentiability and Methods of Differentiation
Exercise 10.3 | Q 22 | 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) = t³ cos t

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

y = `sinx/x^2`

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

Differentiate the following:

y = `x"e"^(-x^2)`

Differentiate the following:
y = sin²(cos kx)

Differentiate the following:
y = `sqrt(x +sqrt(x)`

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

Differentiate the following:

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

Find the derivatives of the following:

(cos x)^{log x}