Advertisements
Advertisements
प्रश्न
Find the derivatives of the following:
`tan^-1 = ((6x)/(1 - 9x^2))`
Advertisements
उत्तर
Let y = `tan^-1 ((6x)/(1 - 9x^2))`
y = `tan^-1 ((2 xx 3x)/(1 - (3x)^2))` ........(1)
Put 3x = tan θ
(1) ⇒ y = `tan^-1 ((2 xx tan theta)/(1 - tan^2 theta))`
y = `tan^-1 (tan 2theta)`
y = 2θ
`("d"y)/("d"theta) = 2 xx 1` = 2 ........(2)
3x = tan θ
`3 ("d"x)/("d"theta) = sec^2theta`
`3 ("d"x)/("d"theta) = 1 + tan^2 theta`
`("d"x)/("d"theta) = 1/3 (1 + (3x)^2)`
`("d"x)/("d"theta) = 1/3 (1 + 9x^2)` .........(3)
Using equation (2) and (3) we have
`(("d"y)/("d"theta))/(("d"x)/("d"theta)) = 2/(1/3 (1 + 9x^2))`
`("d"y)/("d"x) = 6/(1 + 9x^2)`
APPEARS IN
संबंधित प्रश्न
Find the derivatives of the following functions with respect to corresponding independent variables:
y = cos x – 2 tan x
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 = sin x0
Differentiate the following:
y = (x2 + 4x + 6)5
Differentiate the following:
f(t) = `root(3)(1 + tan "t")`
Differentiate the following:
y = cos (a3 + x3)
Differentiate the following:
y = `sin(tan(sqrt(sinx)))`
Find the derivatives of the following:
xy = yx
Find the derivatives of the following:
`sqrt(x^2 + y^2) = tan^-1 (y/x)`
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:
Find the derivative of `sin^-1 ((2x)/(1 + x^2))` with respect to `tan^-1 x`
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)`
Find the derivatives of the following:
If y = sin–1x then find y”
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"`
Choose the correct alternative:
If y = `1/("a" - z)`, then `("d"z)/("d"y)` is
Choose the correct alternative:
`"d"/("d"x) ("e"^(x + 5log x))` is
Choose the correct alternative:
If the derivative of (ax – 5)e3x at x = 0 is – 13, then the value of a 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) = `{{:(2"a" - x, "for" - "a" < x < "a"),(3x - 2"a", "for" x ≥ "a"):}` , then which one of the following is true?
