Advertisements
Advertisements
प्रश्न
Find the derivatives of the following:
If y = `(sin^-1 x)/sqrt(1 - x^2)`, show that (1 – x2)y2 – 3xy1 – y = 0
Advertisements
उत्तर
y = `(sin^-1 x)/sqrt(1 - x^2)`
`y sqrt(1 - x^2) = sin^-1x`
Differentiating with respect to x
`y xx 1/2 (1 - x^2)^(1/2 - 1) (- 2x) + sqrt(1 x^2) y_1 = 1/sqrt(1 - x^2)`
`- xy(1 - x^2)^(- 1/2) + sqrt(1 - x^2) y_1 = 1/sqrt(1 - x^2)`
`(1 - x^2)^(1/2) [- xy(1 - x^2)^(- 1/2) + (1 - x^2)^(1/2) y_1]` = 1
`- xy (1 - x^2)^(- 1/2) xx (1 - x^2)^(1/2) + (1 - x^2)^(- 1/2) * (1 - x^2)^(1/2) y_1` = 1
`- xy + (1 - x^2) y_1` = 1
Differentiating with respect to x, we get
`- x * y_1 + y(-1) + (1 - x^2)y_2 + y_1 (0 - 2x)` = 0
`- xy_1 - y + (1 - x^2)y_2 - 2xy_1` = 0
`(1 - x^2)y_2 - 3xy_1 - y` = 0
APPEARS IN
संबंधित प्रश्न
Find the derivatives of the following functions with respect to corresponding independent variables:
f(x) = x – 3 sin x
Find the derivatives of the following functions with respect to corresponding independent variables:
g(t) = 4 sec t + tan t
Find the derivatives of the following functions with respect to corresponding independent variables:
y = `(tanx - 1)/secx`
Differentiate the following:
y = cos (tan x)
Differentiate the following:
s(t) = `root(4)(("t"^3 + 1)/("t"^3 - 1)`
Differentiate the following:
f(x) = `x/sqrt(7 - 3x)`
Differentiate the following:
y = tan (cos x)
Differentiate the following:
y = `(sin^2x)/cos x`
Differentiate the following:
y = sin3x + cos3x
Differentiate the following:
y = (1 + cos2)6
Find the derivatives of the following:
xy = yx
Find the derivatives of the following:
`sqrt(x^2 + y^2) = tan^-1 (y/x)`
Find the derivatives of the following:
`tan^-1 = ((6x)/(1 - 9x^2))`
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:
Find the derivative with `tan^-1 ((sinx)/(1 + cos x))` with respect to `tan^-1 ((cosx)/(1 + sinx))`
Find the derivatives of the following:
If y = etan–1x, show that (1 + x2)y” + (2x – 1)y’ = 0
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"`
Find the derivatives of the following:
If sin y = x sin(a + y), the prove that `("d"y)/("d"x) = (sin^2("a" + y))/sin"a"`, a ≠ nπ
Choose the correct alternative:
If y = `1/("a" - z)`, then `("d"z)/("d"y)` is
Choose the correct alternative:
`"d"/("d"x) ("e"^(x + 5log x))` is
