Differentiate the following: y = sin2xcosx

Differentiate the following:

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

Sum

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

`("d"y)/("d"x) = (cosx(2sinx cos x) - sin^2x xx - sin x)/(cos x)^2`

`("d"y)/("d"x) = (2sinx cos^2x + sin^3x)/(cos^2x)`

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

= `sin x((2cos2x)/(cos^2x) + (sin2x)/(cos2x))`

= sin x(2 + tan²x)

= sin x(1 + 1 + tan²x)

`("d"y)/("d"x)` = sin x(1 + sec² 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 163]

Chapter 10 Differential Calculus - Differentiability and Methods of Differentiation
Exercise 10.3 | Q 19 | 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:

g(t) = 4 sec t + tan t

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

y = cosec x . cot x

Differentiate the following:
y = (x² + 4x + 6)⁵

Differentiate the following:
y = tan 3x

Differentiate the following:
y = cos (a³ + x³)

Differentiate the following:

y = `"e"^(3x)/(1 + "e"^x`

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

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:

(cos x)^{log x}