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 sin x
Find the derivatives of the following functions with respect to corresponding independent variables:
y = `(tanx - 1)/secx`
Find the derivatives of the following functions with respect to corresponding independent variables:
y = cosec x . cot x
Differentiate the following:
y = cos (tan x)
Differentiate the following:
F(x) = (x3 + 4x)7
Differentiate the following:
y = cos (a3 + x3)
Differentiate the following:
y = 4 sec 5x
Differentiate the following:
y = (2x – 5)4 (8x2 – 5)–3
Differentiate the following:
s(t) = `root(4)(("t"^3 + 1)/("t"^3 - 1)`
Differentiate the following:
y = sin3x + cos3x
Differentiate the following:
y = sin2(cos kx)
Differentiate the following:
y = `sin(tan(sqrt(sinx)))`
Find the derivatives of the following:
(cos x)log x
Find the derivatives of the following:
`tan^-1sqrt((1 - cos x)/(1 + cos x)`
Find the derivatives of the following:
`tan^-1 ((cos x + sin x)/(cos x - sin x))`
Find the derivatives of the following:
If u = `tan^-1 (sqrt(1 + x^2) - 1)/x` and v = `tan^-1 x`, find `("d"u)/("d"v)`
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:
The differential coefficient of `log_10 x` with respect to `log_x 10` is
Choose the correct alternative:
If y = `(1 - x)^2/x^2`, then `("d"y)/("d"x)` is
