Advertisements
Advertisements
प्रश्न
`cos(tan sqrt(x + 1))`
Advertisements
उत्तर
Let y = `cos(tan sqrt(x + 1))`
`"dy"/"dx" = "d"/"dx" cos(tan sqrt(x + 1))`
= `- sin(tan sqrt(x + 1)) "d"/"dx" (tan sqrt(x + 1))`
= `-sin(tan sqrt(x + 1))sec^2 sqrt(x + 1) * "d"/"d"(x + 1)^(1/2)`
= `-sin(tan sqrt(x + 1))sec^2 sqrt(x + 1) 1/2 (sqrt(x + 1))^((-1)/2)`
∴ `(-1)/(2sqrt(x + 1)) * sin(tan sqrt(x + 1)) * sec^2 (sqrt(x + 1))`
APPEARS IN
संबंधित प्रश्न
Differentiate the function with respect to x.
sin (x2 + 5)
Differentiate the function with respect to x.
cos (sin x)
Differentiate the function with respect to x.
`(sin (ax + b))/cos (cx + d)`
Differentiate the function with respect to x.
cos x3 . sin2 (x5)
Differentiate the function with respect to x.
`cos (sqrtx)`
Differentiate the function with respect to x:
sin3 x + cos6 x
Differentiate the function with respect to x:
`(cos^(-1) x/2)/sqrt(2x+7)`, −2 < x < 2
Differentiate the function with respect to x:
`x^(x^2 -3) + (x -3)^(x^2)`, for x > 3
If f(x) = |x|3, show that f"(x) exists for all real x and find it.
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)`
Differentiate `tan^-1 (sqrt(1 - x^2)/x)` with respect to`cos^-1(2xsqrt(1 - x^2))`, where `x ∈ (1/sqrt(2), 1)`
Differential coefficient of sec (tan–1x) w.r.t. x is ______.
cos |x| is differentiable everywhere.
`sin sqrt(x) + cos^2 sqrt(x)`
sinn (ax2 + bx + c)
`sin^-1 1/sqrt(x + 1)`
(sin x)cosx
(x + 1)2(x + 2)3(x + 3)4
`cos^-1 ((sinx + cosx)/sqrt(2)), (-pi)/4 < x < pi/4`
`tan^-1 (sqrt((1 - cosx)/(1 + cosx))), - pi/4 < x < pi/4`
`tan^-1 (secx + tanx), - pi/2 < x < pi/2`
`tan^-1 ((3"a"^2x - x^3)/("a"^3 - 3"a"x^2)), (-1)/sqrt(3) < x/"a" < 1/sqrt(3)`
If xm . yn = (x + y)m+n, prove that `("d"^2"y")/("dx"^2)` = 0
If k be an integer, then `lim_("x" -> "k") ("x" - ["x"])` ____________.
If `"f"("x") = ("sin" ("e"^("x"-2) - 1))/("log" ("x" - 1)), "x" ne 2 and "f" ("x") = "k"` for x = 2, then value of k for which f is continuous is ____________.
A function is said to be continuous for x ∈ R, if ____________.
If `y = (x + sqrt(1 + x^2))^n`, then `(1 + x^2) (d^2y)/(dx^2) + x (dy)/(dx)` is
`d/(dx)[sin^-1(xsqrt(1 - x) - sqrt(x)sqrt(1 - x^2))]` is equal to
If sin y = x sin (a + y), then value of dy/dx is
If f(x) = `{{:((sin(p + 1)x + sinx)/x,",", x < 0),(q,",", x = 0),((sqrt(x + x^2) - sqrt(x))/(x^(3//2)),",", x > 0):}`
is continuous at x = 0, then the ordered pair (p, q) is equal to ______.
If f(x) = `{{:(ax + b; 0 < x ≤ 1),(2x^2 - x; 1 < x < 2):}` is a differentiable function in (0, 2), then find the values of a and b.
If f(x) = `{{:(x^2"," if x ≥ 1),(x"," if x < 1):}`, then show that f is not differentiable at x = 1.
The set of all points where the function f(x) = x + |x| is differentiable, is ______.
Prove that the greatest integer function defined by f(x) = [x], 0 < x < 3 is not differentiable at x = 1 and x = 2.
