English

Differentiate the following w.r.t.x: cos(x2 + a2) - Mathematics and Statistics

Advertisements
Advertisements

Question

Differentiate the following w.r.t.x: cos(x2 + a2)

Sum

Solution

Let y = cos(x2 + a2)

Differentiating w.r.t. x,we get,

`"dy"/"dx" = "d"/"dx"[cos(x^2 + a^2)]`

= `-sin(x^2 + a^2)."d"/"dx"(x^2 + a^2)`

= –sin(x2 + a2).(2x + 0)

= –2x sin(x2 + a2).

shaalaa.com
Differentiation
  Is there an error in this question or solution?
Chapter 1: Differentiation - Exercise 1.1 [Page 12]

RELATED QUESTIONS

Differentiate the following w.r.t.x: `sqrt(x^2 + 4x - 7)`


Differentiate the following w.r.t.x:

`(sqrt(3x - 5) - 1/sqrt(3x - 5))^5`


Differentiate the following w.r.t.x:

tan[cos(sinx)]


Differentiate the following w.r.t.x: `log[sec (e^(x^2))]`


Differentiate the following w.r.t.x: `log_(e^2) (log x)`


Differentiate the following w.r.t.x:

`(x^3 - 5)^5/(x^3 + 3)^3`


Differentiate the following w.r.t.x:

`sqrt(cosx) + sqrt(cossqrt(x)`


Differentiate the following w.r.t.x: `log(sqrt((1 - sinx)/(1 + sinx)))`


Differentiate the following w.r.t. x : tan–1(log x)


Differentiate the following w.r.t. x : cos–1(1 –x2)


Differentiate the following w.r.t. x : `tan^-1[(1 - tan(x/2))/(1 + tan(x/2))]`


Differentiate the following w.r.t. x : `cot^-1((sin3x)/(1 + cos3x))`


Differentiate the following w.r.t. x : `tan^-1((cos7x)/(1 + sin7x))`


Differentiate the following w.r.t.x:

tan–1 (cosec x + cot x)


Differentiate the following w.r.t. x : `sin^-1((4sinx + 5cosx)/sqrt(41))`


Differentiate the following w.r.t. x : `cos^-1((sqrt(3)cosx - sinx)/(2))`


Differentiate the following w.r.t. x : `sin^-1(2xsqrt(1 - x^2))`


Differentiate the following w.r.t. x :

`cos^-1  ((1 - 9^x))/((1 + 9^x)`


Differentiate the following w.r.t. x : `sin^-1  ((1 - 25x^2)/(1 + 25x^2))`


Differentiate the following w.r.t. x :

`sin^(−1) ((1 − x^3)/(1 + x^3))`


Differentiate the following w.r.t. x : `cot^-1((1 - sqrt(x))/(1 + sqrt(x)))`


Differentiate the following w.r.t. x :

`tan^(−1)[(2^(x + 2))/(1 − 3(4^x))]`


Differentiate the following w.r.t. x : `tan^-1((2^x)/(1 + 2^(2x + 1)))`


Differentiate the following w.r.t. x : `tan^-1((a + btanx)/(b - atanx))`


Differentiate the following w.r.t. x: `x^(tan^(-1)x`


Differentiate the following w.r.t. x : (sin x)x 


Differentiate the following w.r.t. x : `10^(x^(x)) + x^(x(10)) + x^(10x)`


Show that `"dy"/"dx" = y/x` in the following, where a and p are constants: `log((x^20 - y^20)/(x^20 + y^20))` = 20


Solve the following : 

The values of f(x), g(x), f'(x) and g'(x) are given in the following table :

x f(x) g(x) f'(x) fg'(x)
– 1 3 2 – 3 4
2 2 – 1 – 5 – 4

Match the following :

A Group – Function B Group – Derivative
(A)`"d"/"dx"[f(g(x))]"at" x = -1` 1.  – 16
(B)`"d"/"dx"[g(f(x) - 1)]"at" x = -1` 2.     20
(C)`"d"/"dx"[f(f(x) - 3)]"at" x = 2` 3.  – 20
(D)`"d"/"dx"[g(g(x))]"at"x = 2` 5.     12

Differentiate y = `sqrt(x^2 + 5)` w.r. to x


Differentiate y = etanx w.r. to x


If y = `sqrt(cos x + sqrt(cos x + sqrt(cos x + ...... ∞)`, show that `("d"y)/("d"x) = (sin x)/(1 - 2y)`


If f(x) = `(3x + 1)/(5x - 4)` and t = `(5 + 3x)/(x - 4)`, then f(t) is ______ 


If x2 + y2 - 2axy = 0, then `dy/dx` equals ______ 


Find `(dy)/(dx)`, if x3 + x3y + xy2 + y3 = 81


Differentiate `tan^-1 (sqrt((3 - x)/(3 + x)))` w.r.t. x.


If `cos((x^2 - y^2)/(x^2 + y^2))` = log a, show that `dy/dx = y/x`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×