English

If f(x) is odd and differentiable, then f′(x) is - Mathematics and Statistics

Advertisements
Advertisements

Question

If f(x) is odd and differentiable, then f′(x) is

One Line Answer

Solution

If f(x) is odd and differentiable, then f′(x) is an even function.

shaalaa.com
Differentiation
  Is there an error in this question or solution?
Chapter 2.1: Differentiation - Very Short Answers

APPEARS IN

RELATED QUESTIONS

Differentiate the following w.r.t.x:

`(2x^(3/2) - 3x^(4/3) - 5)^(5/2)`


Differentiate the following w.r.t.x: `sqrt(tansqrt(x)`


Differentiate the following w.r.t.x: `"cosec"(sqrt(cos x))`


Differentiate the following w.r.t.x: cos2[log(x2 + 7)]


Differentiate the following w.r.t.x: sec[tan (x4 + 4)]


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


Differentiate the following w.r.t.x:

sin2x2 – cos2x2 


Differentiate the following w.r.t.x:

(x2 + 4x + 1)3 + (x3− 5x − 2)4 


Differentiate the following w.r.t.x:

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


Differentiate the following w.r.t.x:

log (sec 3x+ tan 3x)


Differentiate the following w.r.t.x:

`(e^(2x) - e^(-2x))/(e^(2x) + e^(-2x))`


Differentiate the following w.r.t.x:

`log(sqrt((1 - cos3x)/(1 + cos3x)))`


Differentiate the following w.r.t.x:

`log[a^(cosx)/((x^2 - 3)^3 logx)]`


Differentiate the following w.r.t.x:

y = (25)log5(secx) − (16)log4(tanx) 


Differentiate the following w.r.t.x:

`(x^2 + 2)^4/(sqrt(x^2 + 5)`


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


Differentiate the following w.r.t. x :

cos3[cos–1(x3)]


Differentiate the following w.r.t. x : `sin^4[sin^-1(sqrt(x))]`


Differentiate the following w.r.t. x :

`cos^-1(sqrt(1 - cos(x^2))/2)`


Differentiate the following w.r.t. x :

`cot^-1[(sqrt(1 + sin  ((4x)/3)) + sqrt(1 - sin  ((4x)/3)))/(sqrt(1 + sin  ((4x)/3)) - sqrt(1 - sin  ((4x)/3)))]`


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


Differentiate the following w.r.t. x :

`cos^-1[(3cos(e^x) + 2sin(e^x))/sqrt(13)]`


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


Differentiate the following w.r.t. x : cos–1(3x – 4x3)


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


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


Differentiate the following w.r.t.x:

`cot^-1((1 + 35x^2)/(2x))`


Differentiate the following w.r.t. x : `root(3)((4x - 1)/((2x + 3)(5 - 2x)^2)`


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


Show that `"dy"/"dx" = y/x` in the following, where a and p are constants : `e^((x^7 - y^7)/(x^7 + y^7)` = a


Differentiate y = etanx w.r. to x


Differentiate `tan^-1((8x)/(1 - 15x^2))` 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 y = `sin^-1[("a"cosx - "b"sinx)/sqrt("a"^2 + "b"^2)]`, then find `("d"y)/("d"x)`


y = {x(x - 3)}2 increases for all values of x lying in the interval.


Solve `x + y (dy)/(dx) = sec(x^2 + y^2)`


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


Diffierentiate: `tan^-1((a + b cos x)/(b - a cos x))` w.r.t.x.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×