हिंदी

Differentiate the following w.r.t. x : sin-1 (1-25x21+25x2)

Advertisements
Advertisements

प्रश्न

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

योग
Advertisements

उत्तर

Let y = `sin^-1  ((1 - 25x^2)/(1 + 25x^2))`

= `sin^-1[(1 - (5x)^2)/(1 + (5x)^2)]`
Put 5x = tanθ.
Then θ = tan–1(5x)

∴ y = `sin^-1((1 - tan^2θ)/(1 + tan^2θ))`
= sin–1(cos2θ)

= `sin^-1[sin(pi/2 - 2θ)]`

= `pi/(2) - 2θ`

= `pi/(2) - 2tan^-1(5x)`
Differentiating w.r.t. x, we get
∴ `"dy"/"dx" = "d"/"dx"[pi/2 - 2tan^-1 (5x)]`

= `"d"/"dx"(pi/2) - 2"d"/"dx"[tan^-1(5x)]`

= `0 - 2 xx (1)/(1 + (5)^2)."d"/"dx"(5x)`

= `(-2)/(1 + 25x^2) xx 5`

= `(-10)/(1 + 25x^2)`.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Differentiation - Exercise 1.2 [पृष्ठ ३०]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Arts and Science) [English] Standard 12 Maharashtra State Board
अध्याय 1 Differentiation
Exercise 1.2 | Q 9.09 | पृष्ठ ३०

संबंधित प्रश्न

Differentiate the following w.r.t. x:

(x3 – 2x – 1)5


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


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


Differentiate the following w.r.t.x: `log[tan(x/2)]`


Differentiate the following w.r.t.x: `5^(sin^3x + 3)`


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


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


Differentiate the following w.r.t.x: [log {log(logx)}]2


Differentiate the following w.r.t.x: (1 + 4x)5 (3 + x −x2)


Differentiate the following w.r.t.x: (1 + sin2 x)2 (1 + cos2 x)3 


Differentiate the following w.r.t.x:

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


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


Differentiate the following w.r.t.x:

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


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


Differentiate the following w.r.t.x: `log[4^(2x)((x^2 + 5)/(sqrt(2x^3 - 4)))^(3/2)]`


Differentiate the following w.r.t.x:

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


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


Differentiate the following w.r.t. x : `"cosec"^-1[1/cos(5^x)]`


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


Differentiate the following w.r.t. x : `tan^-1[(1 + cos(x/3))/(sin(x/3))]`


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


Differentiate the following w.r.t.x:

tan–1 (cosec x + cot x)


Differentiate the following w.r.t. x : `"cosec"^-1[(10)/(6sin(2^x) - 8cos(2^x))]`


Differentiate the following w.r.t. x :

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


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


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


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


Differentiate the following w.r.t. x : `cot^-1((a^2 - 6x^2)/(5ax))`


Differentiate the following w.r.t. x :

`tan^-1((5 -x)/(6x^2 - 5x - 3))`


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


Differentiate the following w.r.t. x :

`(x +  1)^2/((x + 2)^3(x + 3)^4`


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


Differentiate the following w.r.t. x : `((x^2 + 2x + 2)^(3/2))/((sqrt(x) + 3)^3(cosx)^x`


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


Differentiate the following w.r.t. x: xe + xx + ex + ee.


Differentiate the following w.r.t. x : `x^(e^x) + (logx)^(sinx)`


Differentiate the following w.r.t. x : `[(tanx)^(tanx)]^(tanx) "at"  x = pi/(4)`


Show that `"dy"/"dx" = y/x` in the following, where a and p are constants : `sin((x^3 - y^3)/(x^3 + y^3))` = a3 


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 `sin^-1((2cosx + 3sinx)/sqrt(13))` 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 = `(3x^2 - 4x + 7.5)^4, "then"  dy/dx` is ______ 


Let f(x) = `(1 - tan x)/(4x - pi), x ne pi/4, x ∈ [0, pi/2]`. If f(x) is continuous in `[0, pi/2]`, then f`(pi/4)` is ______.


The value of `d/(dx)[tan^-1((a - x)/(1 + ax))]` is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×