Advertisements
Advertisements
प्रश्न
Differentiate the following w.r.t.x:
`cot^-1((1 + 35x^2)/(2x))`
Advertisements
उत्तर
Let y = `cot^-1((1 + 35x^2)/(2x))`
= `tan^-1((2x)/(1 + 35x^2)) ...[∵ cot^-1 x = tan^-1(1/x)]`
= `tan^-1[(7x - 5x)/(1 + (7x)(5x))]`
= tan–1(7x) – tan–1(5x)
Differentiating w.r.t.x, we get
`(dy)/dx = d/dx [tan^-1 (7x) - tan^-1(5x)]`
= `d/dx [tan^-1(7x)] - d/dx [tan^-1(5x)]`
= `1/(1 + (7x)^2) * d/dx (7x) - 1/(1 + (5x)^2) * d/dx (5x)`
= `1/(1 + 49x^2) xx 7 - 1/(1 + 25x^2) xx 5`
= `7/(1 + 49x^2) - 5/(1 + 25x^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:
`(sqrt(3x - 5) - 1/sqrt(3x - 5))^5`
Differentiate the following w.r.t.x: cos(x2 + a2)
Differentiate the following w.r.t.x: `log[tan(x/2)]`
Differentiate the following w.r.t.x: `e^(3sin^2x - 2cos^2x)`
Differentiate the following w.r.t.x: `log[sec (e^(x^2))]`
Differentiate the following w.r.t.x: `x/(sqrt(7 - 3x)`
Differentiate the following w.r.t.x: `cot(logx/2) - log(cotx/2)`
Differentiate the following w.r.t.x: log[tan3x.sin4x.(x2 + 7)7]
Differentiate the following w.r.t.x: `log(sqrt((1 - sinx)/(1 + sinx)))`
Differentiate the following w.r.t.x: `log[(ex^2(5 - 4x)^(3/2))/root(3)(7 - 6x)]`
Differentiate the following w.r.t.x:
y = (25)log5(secx) − (16)log4(tanx)
Differentiate the following w. r. t. x.
cos–1(1 – x2)
Differentiate the following w.r.t. x : `cot^-1[cot(e^(x^2))]`
Differentiate the following w.r.t. x : `tan^-1[(1 - tan(x/2))/(1 + tan(x/2))]`
Differentiate the following w.r.t. x : `tan^-1[(1 + cos(x/3))/(sin(x/3))]`
Differentiate the following w.r.t. x : `cot^-1((sin3x)/(1 + cos3x))`
Differentiate the following w.r.t. x :
`cot^-1[(sqrt(1 + sin ((4x)/3)) + sqrt(1 - sin ((4x)/3)))/(sqrt(1 + sin ((4x)/3)) - sqrt(1 - sin ((4x)/3)))]`
Differentiate the following w.r.t. x : `sin^-1((4sinx + 5cosx)/sqrt(41))`
Differentiate the following w.r.t. x : `sin^-1((cossqrt(x) + sinsqrt(x))/sqrt(2))`
Differentiate the following w.r.t. x :
`cos^-1[(3cos(e^x) + 2sin(e^x))/sqrt(13)]`
Differentiate the following w.r.t. x : `tan^-1((2x)/(1 - x^2))`
Differentiate the following w.r.t. x : cos–1(3x – 4x3)
Differentiate the following w.r.t. x : `cos^-1((e^x - e^(-x))/(e^x + e^(-x)))`
Differentiate the following w.r.t. x : `tan^-1((2sqrt(x))/(1 + 3x))`
Differentiate the following w.r.t. x : `tan^-1((a + btanx)/(b - atanx))`
Differentiate the following w.r.t. x : `cot^-1((a^2 - 6x^2)/(5ax))`
Differentiate the following w.r.t. x :
`tan^-1((5 -x)/(6x^2 - 5x - 3))`
Differentiate the following w.r.t. x : `cot^-1((4 - x - 2x^2)/(3x + 2))`
Differentiate the following w.r.t. x :
`(x + 1)^2/((x + 2)^3(x + 3)^4`
Differentiate the following w.r.t. x : (sin x)x
Differentiate the following w.r.t. x: xe + xx + ex + ee.
Differentiate the following w.r.t. x : (logx)x – (cos x)cotx
Differentiate the following w.r.t. x :
(sin x)tanx + (cos x)cotx
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 : `sec((x^5 + y^5)/(x^5 - y^5))` = a2
Show that `"dy"/"dx" = y/x` in the following, where a and p are constants : `tan^-1((3x^2 - 4y^2)/(3x^2 + 4y^2))` = a2
If y is a function of x and log (x + y) = 2xy, then the value of y'(0) = ______.
Differentiate y = etanx w.r. to x
If y = `sin^-1[("a"cosx - "b"sinx)/sqrt("a"^2 + "b"^2)]`, then find `("d"y)/("d"x)`
If y = `1 + x + x^2/(2!) + x^3/(3!) + x^4/(4!) + .....,` then `(d^2y)/(dx^2)` = ______
A particle moves so that x = 2 + 27t - t3. The direction of motion reverses after moving a distance of ______ units.
If y = `(3x^2 - 4x + 7.5)^4, "then" dy/dx` is ______
If y = cosec x0, then `"dy"/"dx"` = ______.
Find `(dy)/(dx)`, if x3 + x2y + xy2 + y3 = 81
If x = eθ, (sin θ – cos θ), y = eθ (sin θ + cos θ) then `dy/dx` at θ = `π/4` is ______.
