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:
f(x) = x – 3 sin x
Find the derivatives of the following functions with respect to corresponding independent variables:
y = sin x + cos x
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 = (x2 + 5) log(1 + x) e–3x
Differentiate the following:
y = sin (ex)
Differentiate the following:
y = `5^((-1)/x)`
Differentiate the following:
y = sin2(cos kx)
Find the derivatives of the following:
y = `x^(cosx)`
Find the derivatives of the following:
`sqrt(x) = "e"^((x - y))`
Find the derivatives of the following:
(cos x)log x
Find the derivatives of the following:
`cos[2tan^-1 sqrt((1 - x)/(1 + 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:
If y = `(sin^-1 x)/sqrt(1 - x^2)`, show that (1 – x2)y2 – 3xy1 – y = 0
Find the derivatives of the following:
If sin y = x sin(a + y), the prove that `("d"y)/("d"x) = (sin^2("a" + y))/sin"a"`, a ≠ nπ
Choose the correct alternative:
`"d"/("d"x) (2/pi sin x^circ)` is
Choose the correct alternative:
If y = `1/4 u^4`, u = `2/3 x^3 + 5`, then `("d"y)/("d"x)` is
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) = `{{:(2"a" - x, "for" - "a" < x < "a"),(3x - 2"a", "for" x ≥ "a"):}` , then which one of the following is true?
