Advertisements
Advertisements
प्रश्न
Differentiate the following w.r.t. x : `cot^-1((4 - x - 2x^2)/(3x + 2))`
उत्तर
Let y = `cot^-1((4 - x - 2x^2)/(3x + 2))`
= `tan^-1((3x + 2)/(4 - x - 2x^2)) ...[∵ cot^-1 x = tan^-1(1/x)]`
= `tan^-1[(3x + 2)/(1 - (2x^2 + x - 3))]`
= `tan^-1 [((2x + 3) + (x - 1))/(1 - (2x + 3)(x - 1))]`
= tan–1(2x + 3) + tan–1(x – 1)
Differentiating w.r.t. x, we get
`"dy"/"dx" = "d"/"dx"[tan^-1(2x + 3) + tan^-1(x - 1)]`
= `"d"/"dx"[tan^-1(2x + 3)] + "d"/"dx"[tan^-1(x - 1)]`
= `(1)/(1 + (2x + 3)^2)."d"/"dx"(2x + 3) + (1)/(1 + (x - 1)^2)."d"/"dx"(x - 1)`
= `(1)/(1 + (2x + 3)^2).(2 xx 1 + 0) + (1)/(1 + (x - 1)^2).(1 - 0)`
= `(2)/(1 + (2x + 3)^2) + (1)/(1 + (x - 1)^2`.
APPEARS IN
संबंधित प्रश्न
Differentiate the following w.r.t.x:
`sqrt(x^2 + sqrt(x^2 + 1)`
Differentiate the following w.r.t.x: `e^(3sin^2x - 2cos^2x)`
Differentiate the following w.r.t.x: `e^(log[(logx)^2 - logx^2]`
Differentiate the following w.r.t.x:
`(e^(2x) - e^(-2x))/(e^(2x) + e^(-2x))`
Differentiate the following w.r.t.x: `log[4^(2x)((x^2 + 5)/(sqrt(2x^3 - 4)))^(3/2)]`
Differentiate the following w.r.t.x:
`log[a^(cosx)/((x^2 - 3)^3 logx)]`
Differentiate the following w.r.t.x:
y = (25)log5(secx) − (16)log4(tanx)
Differentiate the following w.r.t.x:
`(x^2 + 2)^4/(sqrt(x^2 + 5)`
Differentiate the following w.r.t. x : cot–1(x3)
Differentiate the following w.r.t. x :
`sin^-1(sqrt((1 + x^2)/2))`
Differentiate the following w.r.t. x :
cos3[cos–1(x3)]
Differentiate the following w.r.t. x : `cot^-1[cot(e^(x^2))]`
Differentiate the following w.r.t. x : `cos^-1(sqrt((1 + cosx)/2))`
Differentiate the following w.r.t. x :
`cos^-1(sqrt(1 - cos(x^2))/2)`
Differentiate the following w.r.t. x : `"cosec"^-1[(10)/(6sin(2^x) - 8cos(2^x))]`
Differentiate the following w.r.t. x :
`cos^-1((1 - x^2)/(1 + x^2))`
Differentiate the following w.r.t. x : `sin^-1(2xsqrt(1 - x^2))`
Differentiate the following w.r.t. x : cos–1(3x – 4x3)
Differentiate the following w.r.t.x:
`cot^-1((1 + 35x^2)/(2x))`
Differentiate the following w.r.t. x : `tan^-1((2sqrt(x))/(1 + 3x))`
Differentiate the following w.r.t. x : `cot^-1((a^2 - 6x^2)/(5ax))`
Differentiate the following w.r.t. x : `root(3)((4x - 1)/((2x + 3)(5 - 2x)^2)`
Differentiate the following w.r.t. x : (sin x)x
Differentiate the following w.r.t. x : `x^(e^x) + (logx)^(sinx)`
Differentiate the following w.r.t. x :
(sin x)tanx + (cos x)cotx
Differentiate the following w.r.t. x : `[(tanx)^(tanx)]^(tanx) "at" x = pi/(4)`
Show that `bb("dy"/"dx" = y/x)` in the following, where a and p are constant:
xpy4 = (x + y)p+4, p ∈ N
Show that `"dy"/"dx" = y/x` in the following, where a and p are constants: `log((x^20 - y^20)/(x^20 + y^20))` = 20
Show that `"dy"/"dx" = y/x` in the following, where a and p are constants : `e^((x^7 - y^7)/(x^7 + y^7)` = a
If y is a function of x and log (x + y) = 2xy, then the value of y'(0) = ______.
Differentiate `cot^-1((cos x)/(1 + sinx))` w.r. to x
If f(x) = 3x - 2 and g(x) = x2, then (fog)(x) = ________.
If x = `sqrt("a"^(sin^-1 "t")), "y" = sqrt("a"^(cos^-1 "t")), "then" "dy"/"dx"` = ______
y = {x(x - 3)}2 increases for all values of x lying in the interval.
If f(x) = `(3x + 1)/(5x - 4)` and t = `(5 + 3x)/(x - 4)`, then f(t) is ______
If y = log (sec x + tan x), find `dy/dx`.
