Advertisements
Advertisements
Question
Find the derivatives of the following:
Find the derivative of `sin^-1 ((2x)/(1 + x^2))` with respect to `tan^-1 x`
Advertisements
Solution
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
RELATED QUESTIONS
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 = `x/(sin x + cosx)`
Find the derivatives of the following functions with respect to corresponding independent variables:
y = `sinx/x^2`
Find the derivatives of the following functions with respect to corresponding independent variables:
y = (x2 + 5) log(1 + x) e–3x
Find the derivatives of the following functions with respect to corresponding independent variables:
y = log10 x
Differentiate the following:
y = cos (tan x)
Differentiate the following:
y = `"e"^sqrt(x)`
Differentiate the following:
s(t) = `root(4)(("t"^3 + 1)/("t"^3 - 1)`
Differentiate the following:
y = (1 + cos2)6
Find the derivatives of the following:
y = `x^(cosx)`
Find the derivatives of the following:
tan (x + y) + tan (x – y) = x
Find the derivatives of the following:
`cos[2tan^-1 sqrt((1 - x)/(1 + x))]`
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 with `tan^-1 ((sinx)/(1 + cos x))` with respect to `tan^-1 ((cosx)/(1 + sinx))`
Find the derivatives of the following:
If y = `(sin^-1 x)/sqrt(1 - x^2)`, show that (1 – x2)y2 – 3xy1 – y = 0
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:
The differential coefficient of `log_10 x` with respect to `log_x 10` 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
