Advertisements
Advertisements
प्रश्न
Find `bb(dy/dx)` in the following:
y = `cos^(-1) ((1-x^2)/(1+x^2))`, 0 < x < 1
Advertisements
उत्तर
y = `cos^-1 ((1 - x^2)/(1 + x^2))`
Let, x = tan θ
⇒ θ = tan−1 x
∴ y = `cos^-1 ((1 - tan^2 theta)/(1 + tan^2 theta))`
= cos−1 (cos 2 θ)
= 2 θ
= 2 tan−1 x
On differentiating with respect to x,
`dy/dx = 2 d/dx tan^-1 x`
`dy/dx = 2 xx 1/(1 + x^2)`
`dy/dx = 2/(1 + x^2)`
APPEARS IN
संबंधित प्रश्न
Differentiate `cos^-1((3cosx-2sinx)/sqrt13)` w. r. t. x.
If `sec((x+y)/(x-y))=a^2. " then " (d^2y)/dx^2=........`
(a) y
(b) x
(c) y/x
(d) 0
Differentiate `tan^(-1)(sqrt(1-x^2)/x)` with respect to `cos^(-1)(2xsqrt(1-x^2))` ,when `x!=0`
Find : ` d/dx cos^−1 ((x−x^(−1))/(x+x^(−1)))`
Find the derivative of the following function f(x) w.r.t. x, at x = 1 :
`f(x)=cos^-1[sin sqrt((1+x)/2)]+x^x`
Find `bb(dy/dx)` in the following:
`y = tan^(-1) ((3x -x^3)/(1 - 3x^2)), - 1/sqrt3 < x < 1/sqrt3`
Find `bb(dy/dx)` in the following:
y = `sin^(-1) ((1-x^2)/(1+x^2))`, 0 < x < 1
Find `bb(dy/dx)` in the following:
y = `sin^(-1)(2xsqrt(1-x^2)), -1/sqrt2 < x < 1/sqrt2`
Find `bb(dy/dx)` in the following:
y = `sec^(-1) (1/(2x^2 - 1)), 0 < x < 1/sqrt2`
Find `dy/dx`, if y = `sin^-1 x + sin^-1 sqrt (1 - x^2)`, 0 < x < 1.
If `xsqrt(1+y) + y sqrt(1+x) = 0`, for, −1 < x < 1, prove that `dy/dx = -1/(1+ x)^2`.
If `sqrt(1-x^2) + sqrt(1- y^2)` = a(x − y), show that dy/dx = `sqrt((1-y^2)/(1-x^2))`
Find the approximate value of tan−1 (1.001).
Differentiate `tan^(-1) ((1+cosx)/(sin x))` with respect to x
if `x = tan(1/a log y)`, prove that `(1+x^2) (d^2y)/(dx^2) + (2x + a) (dy)/(dx) = 0`
Solve `cos^(-1)(sin cos^(-1)x) = pi/2`
If y = cos (sin x), show that: `("d"^2"y")/("dx"^2) + "tan x" "dy"/"dx" + "y" "cos"^2"x" = 0`
If y = sin-1 x + cos-1x find `(dy)/(dx)`.
If `log (x^2 + y^2) = 2 tan^-1 (y/x)`, show that `(dy)/(dx) = (x + y)/(x - y)`
If `"y" = (sin^-1 "x")^2, "prove that" (1 - "x"^2) (d^2"y")/(d"x"^2) - "x" (d"y")/(d"x") - 2 = 0`.
If y = `(sin^-1 x)^2,` prove that `(1-x^2) (d^2y)/dx^2 - x dy/dx -2 = 0.`
The function f(x) = cot x is discontinuous on the set ______.
`lim_("h" -> 0) (1/("h"^2 sqrt(8 + "h")) - 1/(2"h"))` is equal to ____________.
`lim_("x"-> 0) ("cosec x - cot x")/"x"` is equal to ____________.
`"d"/"dx" {"cosec"^-1 ((1 + "x"^2)/(2"x"))}` is equal to ____________.
If `"y = sin"^-1 ((sqrt"x" - 1)/(sqrt"x" + 1)) + "sec"^-1 ((sqrt"x" + 1)/(sqrt"x" - 1)), "x" > 0, "then" "dy"/"dx"` is ____________.
If y = sin–1x, then (1 – x2)y2 is equal to ______.
Differentiate `sec^-1 (1/sqrt(1 - x^2))` w.r.t. `sin^-1 (2xsqrt(1 - x^2))`.
