Advertisements
Advertisements
Question
Differentiate the following w.r.t. x : `cot^-1[cot(e^(x^2))]`
Advertisements
Solution
Let y = `cot^-1[cot(e^(x^2))] = e^(x^2)`
Differentiating w.r.t. x, we get
`"dy"/"dx" = "d"/"dx"(e^(x^2))`
= `e^(x^2).("d"(x^2))/"dx"`
= `e^(x^2). 2x`
= `2x.e^(x^2)`.
APPEARS IN
RELATED QUESTIONS
Differentiate the following w.r.t. x:
(x3 – 2x – 1)5
Differentiate the following w.r.t.x:
`(sqrt(3x - 5) - 1/sqrt(3x - 5))^5`
Differentiate the following w.r.t.x:
`sqrt(e^((3x + 2) + 5)`
Differentiate the following w.r.t.x: `"cosec"(sqrt(cos x))`
Differentiate the following w.r.t.x:
tan[cos(sinx)]
Differentiate the following w.r.t.x: `sinsqrt(sinsqrt(x)`
Differentiate the following w.r.t.x: `log_(e^2) (log x)`
Differentiate the following w.r.t.x:
`(x^3 - 5)^5/(x^3 + 3)^3`
Differentiate the following w.r.t.x: `(e^sqrt(x) + 1)/(e^sqrt(x) - 1)`
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 : tan–1(log x)
Differentiate the following w.r.t. x : cot–1(4x)
Differentiate the following w.r.t. x:
`sin^-1(sqrt((1 + x^2)/2))`
Differentiate the following w.r.t. x : `"cosec"^-1[1/cos(5^x)]`
Differentiate the following w.r.t. x : `sin^-1((4sinx + 5cosx)/sqrt(41))`
Differentiate the following w.r.t. x : `cos^-1((sqrt(3)cosx - sinx)/(2))`
Differentiate the following w.r.t. x :
`cos^-1((1 - x^2)/(1 + x^2))`
Differentiate the following w.r.t. x : `sin^-1((1 - x^2)/(1 + x^2))`
Differentiate the following w.r.t. x : `tan^-1((8x)/(1 - 15x^2))`
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 :
`(x + 1)^2/((x + 2)^3(x + 3)^4`
Differentiate the following w.r.t. x : `root(3)((4x - 1)/((2x + 3)(5 - 2x)^2)`
Differentiate the following w.r.t. x: `x^(tan^(-1)x`
Differentiate the following w.r.t. x: xe + xx + ex + ee.
Differentiate the following w.r.t. x:
`x^(x^x) + e^(x^x)`
Differentiate the following w.r.t. x :
etanx + (logx)tanx
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 `"dy"/"dx" = y/x` in the following, where a and p are constants : x7.y5 = (x + y)12
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`
If y = sin−1 (2x), find `("d"y)/(""d"x)`
If y = `"e"^(1 + logx)` then find `("d"y)/("d"x)`
If y = `sqrt(cos x + sqrt(cos x + sqrt(cos x + ...... ∞)`, show that `("d"y)/("d"x) = (sin x)/(1 - 2y)`
If y = `sin^-1[("a"cosx - "b"sinx)/sqrt("a"^2 + "b"^2)]`, then find `("d"y)/("d"x)`
y = {x(x - 3)}2 increases for all values of x lying in the interval.
If y = `(3x^2 - 4x + 7.5)^4, "then" dy/dx` is ______
The volume of a spherical balloon is increasing at the rate of 10 cubic centimetre per minute. The rate of change of the surface of the balloon at the instant when its radius is 4 centimetres, is ______
Find `(dy)/(dx)`, if x3 + x2y + xy2 + y3 = 81
The value of `d/(dx)[tan^-1((a - x)/(1 + ax))]` is ______.
If x = eθ, (sin θ – cos θ), y = eθ (sin θ + cos θ) then `dy/dx` at θ = `π/4` is ______.
Diffierentiate: `tan^-1((a + b cos x)/(b - a cos x))` w.r.t.x.
`lim_(x → 0) (sqrt(1 + x + x^2) − 1)/x` = ______.
