English
Tamil Nadu Board of Secondary EducationHSC Science Class 11

Differentiate the following:y = tan (cos x)

Advertisements
Advertisements

Question

Differentiate the following:
y = tan (cos x)

Sum
Advertisements

Solution

y = tan (cos x)

[y = f(g(x)

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

`("d"y)/("d"x) = sec^2(cos x) xx "d"/("d"x) (cos x)`

= sec2 (cos x) × – sin x

`("d"y)/("d"x)` = – sin x . sec2(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 163]

APPEARS IN

Samacheer Kalvi Mathematics - Volume 1 and 2 [English] Class 11 TN Board
Chapter 10 Differential Calculus - Differentiability and Methods of Differentiation
Exercise 10.3 | Q 18 | Page 163

RELATED QUESTIONS

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:

y = cos x – 2 tan x


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

y = cosec x . cot x


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


Differentiate the following:
y = e–mx 


Differentiate the following:

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


Differentiate the following:
y = `sqrt(1 + 2tanx)`


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


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


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


Find the derivatives of the following:

If cos(xy) = x, show that `(-(1 + ysin(xy)))/(xsiny)`


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 u = `tan^-1  (sqrt(1 + x^2) - 1)/x` and v = `tan^-1 x`, find `("d"u)/("d"v)`


Find the derivatives of the following:

If x = a(θ + sin θ), y = a(1 – cos θ) then prove that at θ = `pi/2`, yn = `1/"a"`


Choose the correct alternative:
If f(x) = x tan-1x then f'(1) is


Choose the correct alternative:

The differential coefficient of `log_10 x` with respect to `log_x 10` is


Choose the correct alternative:

If y = `(1 - x)^2/x^2`, then `("d"y)/("d"x)` is


Choose the correct alternative:

If f(x) = `{{:(2"a" - x,  "for"  - "a" < x < "a"),(3x - 2"a", "for"  x ≥ "a"):}` , then which one of the following is true?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×