Advertisements
Advertisements
प्रश्न
Differentiate the function with respect to x.
cos (sin x)
उत्तर
Let, y = cos (sin x)
Let, sin x = t
∴ y = cos t
`dy/dt = - sin t, dt/dx = cos x`
`∴ dy/dx = dy/dt * dt/dx`
= - sin t · cos x
= - sin t cos x
= - sin (sin x)cos x
APPEARS IN
संबंधित प्रश्न
Differentiate the function with respect to x.
`sec(tan (sqrtx))`
Differentiate the function with respect to x.
`cos (sqrtx)`
Prove that the function f given by `f(x) = |x - 1|, x in R` is not differentiable at x = 1.
Differentiate w.r.t. x the function:
(3x2 – 9x + 5)9
Differentiate w.r.t. x the function:
sin3 x + cos6 x
Differentiate w.r.t. x the function:
`(5x)^(3cos 2x)`
Find `dy/dx, if y = 12 (1 – cos t), x = 10 (t – sin t), -pi/2< t< pi/2`
If f (x) = |x|3, show that f ″(x) exists for all real x and find it.
if y = `[(f(x), g(x), h(x)),(l, m,n),(a,b,c)]`, prove that `dy/dx` =`|(f'(x), g'(x), h'(x)),(l,m, n),(a,b,c)|`
If f(x) = x + 1, find `d/dx (fof) (x)`
If y = tan(x + y), find `("d"y)/("d"x)`
If y = tanx + secx, prove that `("d"^2y)/("d"x^2) = cosx/(1 - sinx)^2`
Differentiate `tan^-1 (sqrt(1 - x^2)/x)` with respect to`cos^-1(2xsqrt(1 - x^2))`, where `x ∈ (1/sqrt(2), 1)`
Let f(x)= |cosx|. Then, ______.
If u = `sin^-1 ((2x)/(1 + x^2))` and v = `tan^-1 ((2x)/(1 - x^2))`, then `"du"/"dv"` is ______.
COLUMN-I | COLUMN-II |
(A) If a function f(x) = `{((sin3x)/x, "if" x = 0),("k"/2",", "if" x = 0):}` is continuous at x = 0, then k is equal to |
(a) |x| |
(B) Every continuous function is differentiable | (b) True |
(C) An example of a function which is continuous everywhere but not differentiable at exactly one point |
(c) 6 |
(D) The identity function i.e. f (x) = x ∀ ∈x R is a continuous function |
(d) False |
|sinx| is a differentiable function for every value of x.
`cos(tan sqrt(x + 1))`
sinx2 + sin2x + sin2(x2)
`sin^-1 1/sqrt(x + 1)`
sinmx . cosnx
`tan^-1 (secx + tanx), - pi/2 < x < pi/2`
`sec^-1 (1/(4x^3 - 3x)), 0 < x < 1/sqrt(2)`
`tan^-1 ((sqrt(1 + x^2) + sqrt(1 - x^2))/(sqrt(1 + x^2) - sqrt(1 - x^2))), -1 < x < 1, x ≠ 0`
The differential coefficient of `"tan"^-1 ((sqrt(1 + "x") - sqrt (1 - "x"))/(sqrt (1+ "x") + sqrt (1 - "x")))` is ____________.
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 ____________.
If `y = (x + sqrt(1 + x^2))^n`, then `(1 + x^2) (d^2y)/(dx^2) + x (dy)/(dx)` is
The rate of increase of bacteria in a certain culture is proportional to the number present. If it doubles in 5 hours then in 25 hours, its number would be
`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 `ysqrt(1 - x^2) + xsqrt(1 - y^2)` = 1, then prove that `(dy)/(dx) = - sqrt((1 - y^2)/(1 - x^2))`
A particle is moving on a line, where its position S in meters is a function of time t in seconds given by S = t3 + at2 + bt + c where a, b, c are constant. It is known that at t = 1 seconds, the position of the particle is given by S = 7 m. Velocity is 7 m/s and acceleration is 12 m/s2. The values of a, b, c are ______.
If f(x) = | cos x |, then `f((3π)/4)` is ______.
Prove that the greatest integer function defined by f(x) = [x], 0 < x < 3 is not differentiable at x = 1 and x = 2.