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) = t3 cos 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 = `tan x/x`
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 = cosec x . cot x
Find the derivatives of the following functions with respect to corresponding independent variables:
y = x sin x cos x
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 = sin (ex)
Differentiate the following:
h(t) = `("t" - 1/"t")^(3/2)`
Differentiate the following:
y = 4 sec 5x
Differentiate the following:
y = (2x – 5)4 (8x2 – 5)–3
Differentiate the following:
y = `(x^2 + 1) root(3)(x^2 + 2)`
Differentiate the following:
y = tan (cos x)
Differentiate the following:
y = sin3x + cos3x
Find the derivatives of the following:
tan (x + y) + tan (x – y) = x
Find the derivatives of the following:
`cos^-1 ((1 - x^2)/(1 + x^2))`
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)`
Choose the correct alternative:
If y = `1/("a" - z)`, then `("d"z)/("d"y)` is
Choose the correct alternative:
If the derivative of (ax – 5)e3x at x = 0 is – 13, then the value of a is
