Differentiate the following:y = sin3x + cos3x

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) = 4 sec t + tan t

Differentiate the following:

y = `(x^2 + 1) root(3)(x^2 + 2)`

Differentiate the following:
y = tan (cos x)

Differentiate the following:

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

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:
y = `x^(cosx)`

Find the derivatives of the following:
x^y = y^x

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:

`cos[2tan^-1 sqrt((1 - x)/(1 + x))]`

Find the derivatives of the following:

Find the derivative of `sin^-1 ((2x)/(1 + x^2))` with respect to `tan^-1 x`

Find the derivatives of the following:

If y = `(sin^-1 x)/sqrt(1 - x^2)`, show that (1 – x²)y₂ – 3xy₁ – y = 0