Advertisements
Advertisements
प्रश्न
Differentiate the following w.r.t. x : `cos^-1(sqrt((1 + cosx)/2))`
Advertisements
उत्तर
Let y = `cos^-1(sqrt((1 + cosx)/2))`
= `cos^-1(sqrt((2cos^2(x/2))/2))`
= `cos^-1[cos(x/2)]`
= `x/(2)`
Differentiating w.r.t. x, we get
`"dy"/"dx" = "d"/"dx"(x/2)`
= `(1)/(2)"d"/"dx"(x)`
= `(1)/(2) xx 1`
= `(1)/(2)`.
APPEARS IN
संबंधित प्रश्न
Differentiate the following w.r.t. x: `sqrt(x^2 + 4x - 7)`.
Differentiate the following w.r.t.x:
`(sqrt(3x - 5) - 1/sqrt(3x - 5))^5`
Differentiate the following w.r.t.x: `log[tan(x/2)]`
Differentiate the following w.r.t.x: `sqrt(tansqrt(x)`
Differentiate the following w.r.t.x: `5^(sin^3x + 3)`
Differentiate the following w.r.t.x: `"cosec"(sqrt(cos x))`
Differentiate the following w.r.t.x: log[cos(x3 – 5)]
Differentiate the following w.r.t.x: [log {log(logx)}]2
Differentiate the following w.r.t.x:
(x2 + 4x + 1)3 + (x3− 5x − 2)4
Differentiate the following w.r.t.x: `x/(sqrt(7 - 3x)`
Differentiate the following w.r.t.x: `(1 + sinx°)/(1 - sinx°)`
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.
cos–1(1 – x2)
Differentiate the following w.r.t. x : `sin^4[sin^-1(sqrt(x))]`
Differentiate the following w.r.t. x :
`cos^-1(sqrt(1 - cos(x^2))/2)`
Differentiate the following w.r.t. x : `tan^-1((cos7x)/(1 + sin7x))`
Differentiate the following w.r.t. x : `tan^-1(sqrt((1 + cosx)/(1 - cosx)))`
Differentiate the following w.r.t. x : `sin^-1((4sinx + 5cosx)/sqrt(41))`
Differentiate the following w.r.t. x : `cos^-1((3cos3x - 4sin3x)/5)`
Differentiate the following w.r.t. x : `"cosec"^-1[(10)/(6sin(2^x) - 8cos(2^x))]`
Differentiate the following w.r.t. x : `sin^-1((1 - x^2)/(1 + x^2))`
Differentiate the following w.r.t. x : `cot^-1((1 - sqrt(x))/(1 + sqrt(x)))`
Differentiate the following w.r.t. x : `tan^-1((8x)/(1 - 15x^2))`
Differentiate the following w.r.t. x : `(x^5.tan^3 4x)/(sin^2 3x)`
Differentiate the following w.r.t. x: xe + xx + ex + ee.
Differentiate the following w.r.t. x:
`x^(x^x) + e^(x^x)`
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 : `cos^-1((7x^4 + 5y^4)/(7x^4 - 5y^4)) = tan^-1a`
Show that `"dy"/"dx" = y/x` in the following, where a and p are constants : `sin((x^3 - y^3)/(x^3 + y^3))` = a3
If y = `"e"^(1 + logx)` then find `("d"y)/("d"x)`
Differentiate `cot^-1((cos x)/(1 + sinx))` w.r. to x
If y = `sin^-1[("a"cosx - "b"sinx)/sqrt("a"^2 + "b"^2)]`, then find `("d"y)/("d"x)`
If f(x) = 3x - 2 and g(x) = x2, then (fog)(x) = ________.
If `t = v^2/3`, then `(-v/2 (df)/dt)` is equal to, (where f is acceleration) ______
y = {x(x - 3)}2 increases for all values of x lying in the interval.
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.
The weight W of a certain stock of fish is given by W = nw, where n is the size of stock and w is the average weight of a fish. If n and w change with time t as n = 2t2 + 3 and w = t2 - t + 2, then the rate of change of W with respect to t at t = 1 is ______
If f(x) = `(3x + 1)/(5x - 4)` and t = `(5 + 3x)/(x - 4)`, then f(t) is ______
Solve `x + y (dy)/(dx) = sec(x^2 + y^2)`
If x = eθ, (sin θ – cos θ), y = eθ (sin θ + cos θ) then `dy/dx` at θ = `π/4` is ______.
Let f(x) be a polynomial function of the second degree. If f(1) = f(–1) and a1, a2, a3 are in AP, then f’(a1), f’(a2), f’(a3) are in ______.
If `cos((x^2 - y^2)/(x^2 + y^2))` = log a, show that `dy/dx = y/x`
