Advertisements
Advertisements
प्रश्न
If u = `sin^-1 ((2x)/(1 + x^2))` and v = `tan^-1 ((2x)/(1 - x^2))`, then `"du"/"dv"` is ______.
विकल्प
`1/2`
x
`(1 - x^2)/(1 + x^2)`
1
उत्तर
If u = `sin^-1 ((2x)/(1 + x^2))` and v = `tan^-1 ((2x)/(1 - x^2))`, then `"du"/"dv"` is 1.
APPEARS IN
संबंधित प्रश्न
Differentiate the function with respect to x.
cos (sin x)
Differentiate the function with respect to x.
`sec(tan (sqrtx))`
Differentiate the function with respect to x.
`2sqrt(cot(x^2))`
Differentiate the function with respect to x.
`cos (sqrtx)`
Differentiate w.r.t. x the function:
(3x2 – 9x + 5)9
Differentiate w.r.t. x the function:
`(cos^(-1) x/2)/sqrt(2x+7), -2 < x < 2`
Find `dy/dx, if y = 12 (1 – cos t), x = 10 (t – sin t), -pi/2< t< pi/2`
If (x – a)2 + (y – b)2 = c2, for some c > 0, prove that `[1+ (dy/dx)^2]^(3/2)/((d^2y)/dx^2)` is a constant independent of a and b.
If f (x) = |x|3, show that f ″(x) exists for all real x and find it.
Does there exist a function which is continuos everywhere but not differentiable at exactly two points? Justify your answer?
Discuss the continuity and differentiability of the
If sin y = xsin(a + y) prove that `(dy)/(dx) = sin^2(a + y)/sin a`
If f(x) = x + 1, find `d/dx (fof) (x)`
Let f(x) = x|x|, for all x ∈ R. Discuss the derivability of f(x) at x = 0
Let f(x)= |cosx|. Then, ______.
|sinx| is a differentiable function for every value of x.
sinn (ax2 + bx + c)
sinx2 + sin2x + sin2(x2)
`tan^-1 ((3"a"^2x - x^3)/("a"^3 - 3"a"x^2)), (-1)/sqrt(3) < x/"a" < 1/sqrt(3)`
For the curve `sqrt(x) + sqrt(y)` = 1, `"dy"/"dx"` at `(1/4, 1/4)` is ______.
A function is said to be continuous for x ∈ R, if ____________.
If `ysqrt(1 - x^2) + xsqrt(1 - y^2)` = 1, then prove that `(dy)/(dx) = - sqrt((1 - y^2)/(1 - x^2))`
Let c, k ∈ R. If f(x) = (c + 1)x2 + (1 – c2)x + 2k and f(x + y) = f(x) + f(y) – xy, for all x, y ∈ R, then the value of |2(f(1) + f(2) + f(3) + ... + f(20))| is equal to ______.
The function f(x) = x | x |, x ∈ R is differentiable ______.
The set of all points where the function f(x) = x + |x| is differentiable, is ______.
