Advertisements
Advertisements
प्रश्न
Find the derivatives of the following:
Find the derivative of `sin^-1 ((2x)/(1 + x^2))` with respect to `tan^-1 x`
Advertisements
उत्तर
Let u = `sin^-1 ((2x)/(1 + x^2))`
Put x = tan θ
u = `sin^-1 ((2tantheta)/(1 + tan^2theta))`
u = `sin^-1 (sin 2theta)`
u = 2θ
u = `2 tan^-1 (x)`
`("du")/("d"x) = 2/(1 + x^2)` ...(1)
Let v = `tan^-1 x`
`("dv")/("d"x) = 2/(1 + x^2)` ...(2)
From equations (1) and (2)
`(("du")/(dx))/(("dv")/(dx)) = (2/(1 + x^2))/(1/(1 + x^2))`
`("du")/("dv")` = 2
`("d"(sin^-1 ((2x)/(1 + x^2))))/("d"(tan^-1 x))` = 2
APPEARS IN
संबंधित प्रश्न
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 = ex sin x
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 = `(tanx - 1)/secx`
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 = cos (tan x)
Differentiate the following:
F(x) = (x3 + 4x)7
Differentiate the following:
y = `x"e"^(-x^2)`
Differentiate the following:
y = `sqrt(1 + 2tanx)`
Differentiate the following:
y = `"e"^(3x)/(1 + "e"^x`
Differentiate the following:
y = `sin(tan(sqrt(sinx)))`
Find the derivatives of the following:
If cos(xy) = x, show that `(-(1 + ysin(xy)))/(xsiny)`
Find the derivatives of the following:
Find the derivative of sin x2 with respect to x2
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:
If f(x) = x tan-1x then f'(1) is
Choose the correct alternative:
If x = a sin θ and y = b cos θ, then `("d"^2y)/("d"x^2)` is
Choose the correct alternative:
If f(x) = `{{:("a"x^2 - "b"",", - 1 < x < 1),(1/|x|",", "elsewhere"):}` is differentiable at x = 1, then
