Advertisements
Advertisements
Question
Differentiate the function with respect to x.
`cos (sqrtx)`
Solution
cos `(sqrtx)`
Let y = cos `(sqrtx)` and `sqrtx` = u.
Then y = cos u
`dy/dx = dy/du xx du/dx`
`= (d cos u)/du xx (d sqrtx)/dx`
`= - sin u xx 1/2 sqrtx`
`= - (sin sqrtx)/(2 sqrtx)`
APPEARS IN
RELATED QUESTIONS
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 x^3. sin^2 (x^5)`
Differentiate the function with respect to x.
`2sqrt(cot(x^2))`
Differentiate w.r.t. x the function:
sin3 x + cos6 x
Differentiate w.r.t. x the function:
`x^(x^2 -3) + (x -3)^(x^2)`, for x > 3
Discuss the continuity and differentiability of the
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`
Differential coefficient of sec (tan–1x) w.r.t. x is ______.
|sinx| is a differentiable function for every value of x.
cos |x| is differentiable everywhere.
sinn (ax2 + bx + c)
`sin^-1 1/sqrt(x + 1)`
`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)`
`tan^-1 ((sqrt(1 + x^2) + sqrt(1 - x^2))/(sqrt(1 + x^2) - sqrt(1 - x^2))), -1 < x < 1, x ≠ 0`
If xm . yn = (x + y)m+n, prove that `("d"^2"y")/("dx"^2)` = 0
If y = `sqrt(sinx + y)`, then `"dy"/"dx"` is equal to ______.
For the curve `sqrt(x) + sqrt(y)` = 1, `"dy"/"dx"` at `(1/4, 1/4)` is ______.
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 ____________.
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
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 ______.
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 ______.
Let f: R→R and f be a differentiable function such that f(x + 2y) = f(x) + 4f(y) + 2y(2x – 1) ∀ x, y ∈ R and f’(0) = 1, then f(3) + f’(3) is ______.
Let S = {t ∈ R : f(x) = |x – π| (e|x| – 1)sin |x| is not differentiable at t}. Then the set S is equal to ______.
Prove that the greatest integer function defined by f(x) = [x], 0 < x < 3 is not differentiable at x = 1 and x = 2.