Differentiate the following:y = sin3x + cos3x - Mathematics

Differentiate the following:
y = sin³x + cos³x

Sum

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)

shaalaa.com

Differentiation Rules

Is there an error in this question or solution?

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 22 | Page 164

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

g(t) = 4 sec t + tan t

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 = e^-x . log x

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

Differentiate the following:
y = 4 sec 5x

Differentiate the following:

y = `(sin^2x)/cos x`

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

Differentiate the following:

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

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