Advertisements
Advertisements
Question
Find the derivatives of the following:
`tan^-1sqrt((1 - cos x)/(1 + cos x)`
Advertisements
Solution
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
RELATED QUESTIONS
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 = `sinx/(1 + cosx)`
Find the derivatives of the following functions with respect to corresponding independent variables:
y = cosec x . cot x
Find the derivatives of the following functions with respect to corresponding independent variables:
y = e-x . log x
Find the derivatives of the following functions with respect to corresponding independent variables:
y = (x2 + 5) log(1 + x) e–3x
Differentiate the following:
y = (x2 + 4x + 6)5
Differentiate the following:
y = `(x^2 + 1) root(3)(x^2 + 2)`
Differentiate the following:
y = tan (cos x)
Differentiate the following:
y = `"e"^(3x)/(1 + "e"^x`
Find the derivatives of the following:
xy = yx
Find the derivatives of the following:
`cos[2tan^-1 sqrt((1 - x)/(1 + x))]`
Find the derivatives of the following:
x = `"a" cos^3"t"` ; y = `"a" sin^3"t"`
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:
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 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 y = `(cos^-1 x)^2`, prove that `(1 - x^2) ("d"^2y)/("d"x)^2 - x ("d"y)/("d"x) - 2` = 0. Hence find y2 when x = 0
Choose the correct alternative:
x = `(1 - "t"^2)/(1 + "t"^2)`, y = `(2"t")/(1 + "t"^2)` then `("d"y)/("d"x)` is
Choose the correct alternative:
If f(x) = `{{:("a"x^2 - "b"",", - 1 < x < 1),(1/|x|",", "elsewhere"):}` is differentiable at x = 1, then
Choose the correct alternative:
The number of points in R in which the function f(x) = |x – 1| + |x – 3| + sin x is not differentiable, is
