Advertisements
Advertisements
प्रश्न
Find the derivatives of the following:
`tan^-1sqrt((1 - cos x)/(1 + cos x)`
Advertisements
उत्तर
Let y = `tan^-1sqrt((1 - cos x)/(1 + cos x)`
[1 – cos 2θ = 2 sin2θ and 1 + cos 2θ = 2 sin2 θ]
y = `tan^-1 sqrt((2 sin^2 x/2)/(2 cos^2 x/2))`
y = `tan^-1 sqrt(tan^2 x/2)`
y = `tan^-1(tan x/2)`
y = `x/2`
`("d"y)/("d"x) = 1/2 xx 1 = 1/2`
APPEARS IN
संबंधित प्रश्न
Find the derivatives of the following functions with respect to corresponding independent variables:
y = cos x – 2 tan x
Find the derivatives of the following functions with respect to corresponding independent variables:
g(t) = t3 cos t
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 = x sin x cos x
Differentiate the following:
y = `(x^2 + 1) root(3)(x^2 + 2)`
Differentiate the following:
y = `sqrt(x +sqrt(x)`
Find the derivatives of the following:
`sqrt(x^2 + y^2) = tan^-1 (y/x)`
Find the derivatives of the following:
tan (x + y) + tan (x – y) = x
Find the derivatives of the following:
x = `(1 - "t"^2)/(1 + "t"^2)`, y = `(2"t")/(1 + "t"^2)`
Find the derivatives of the following:
sin-1 (3x – 4x3)
Find the derivatives of the following:
`tan^-1 ((cos x + sin x)/(cos x - sin x))`
Find the derivatives of the following:
Find the derivative of sin x2 with respect to x2
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 = sin–1x then find y”
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 y = `(sin^-1 x)/sqrt(1 - x^2)`, show that (1 – x2)y2 – 3xy1 – y = 0
Choose the correct alternative:
`"d"/("d"x) (2/pi sin x^circ)` is
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:
The differential coefficient of `log_10 x` with respect to `log_x 10` is
