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:
y = cosec x . cot x
Differentiate the following:
F(x) = (x3 + 4x)7
Differentiate the following:
y = 4 sec 5x
Differentiate the following:
y = `x"e"^(-x^2)`
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 = `"e"^(3x)/(1 + "e"^x`
Differentiate the following:
y = `"e"^(xcosx)`
Find the derivatives of the following:
y = `x^(logx) + (logx)^x`
Find the derivatives of the following:
If cos(xy) = x, show that `(-(1 + ysin(xy)))/(xsiny)`
Find the derivatives of the following:
`tan^-1 = ((6x)/(1 - 9x^2))`
Find the derivatives of the following:
`cos[2tan^-1 sqrt((1 - x)/(1 + x))]`
Find the derivatives of the following:
x = a (cos t + t sin t); y = a (sin t – t cos t)
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 y = etan–1x, show that (1 + x2)y” + (2x – 1)y’ = 0
Choose the correct alternative:
If the derivative of (ax – 5)e3x at x = 0 is – 13, then the value of a is
Choose the correct alternative:
If f(x) = `{{:(x - 5, "if" x ≤ 1),(4x^2 - 9, "if" 1 < x < 2),(3x + 4, "if" x ≥ 2):}` , then the right hand derivative of f(x) at x = 2 is
