Advertisements
Advertisements
Question
If y = `sec^-1 ((sqrt(x) + 1)/(sqrt(x + 1))) + sin^-1((sqrt(x) - 1)/(sqrt(x) + 1))`, then `"dy"/"dx"` is equal to ______.
Solution
If y = `sec^-1 ((sqrt(x) + 1)/(sqrt(x - 1))) + sin^-1((sqrt(x) - 1)/(sqrt(x) + 1))`, then `"dy"/"dx"` is equal to 0.
APPEARS IN
RELATED QUESTIONS
Find `dy/dx if x + sqrt(xy) + y = 1`
Find `"dy"/"dx"` if cos (xy) = x + y
Find the second order derivatives of the following : xx
Find `"dy"/"dx"` if, y = log(10x4 + 5x3 - 3x2 + 2)
If y = 2x2 + 22 + a2, then `"dy"/"dx" = ?`
State whether the following is True or False:
The derivative of polynomial is polynomial.
Solve the following:
If y = (6x3 - 3x2 - 9x)10, find `"dy"/"dx"`
If f'(4) = 5, f(4) = 3, g'(6) = 7 and R(x) = g[3 + f(x)] then R'(4) = ______
Suppose y = f(x) is a differentiable function of x on an interval I and y is one – one, onto and `("d"y)/("d"x)` ≠ 0 on I. Also if f–1(y) is differentiable on f(I), then `("d"x)/("d"y) = 1/(("d"y)/("d"x)), ("d"y)/("d"x)` ≠ 0
If x = f(t) and y = g(t) are differentiable functions of t so that y is a differentiable function of x and `(dx)/(dt)` ≠ 0 then `(dy)/(dx) = ((dy)/(dt))/((dx)/(d"))`.
Hence find `(dy)/(dx)` if x = sin t and y = cost
Choose the correct alternative:
If y = `x^(sqrt(x))`, then `("d"y)/("d"x)` = ?
Find `("d"^2y)/("d"x^2)`, if y = `"e"^((2x + 1))`
Differentiate `sqrt(tansqrt(x))` w.r.t. x
If ex + ey = ex+y , prove that `("d"y)/("d"x) = -"e"^(y - x)`
If x = a sec3θ and y = a tan3θ, find `("d"y)/("d"x)` at θ = `pi/3`
If f(x) = |cos x – sinx|, find `"f'"(pi/6)`
If ax2 + 2hxy + by2 = 0, then prove that `(d^2y)/(dx^2)` = 0.
If y = 2x2 + a2 + 22 then `dy/dx` = ______.
Find `dy/dx` if, y = `e^(5 x^2 - 2x + 4)`
If y = `root5((3x^2 + 8x + 5)^4)`, find `dy/dx`
lf y = f(u) is a differentiable function of u and u = g(x) is a differentiable function of x, such that the composite function y = f[g(x)] is a differentiable function of x, then prove that:
`dy/dx = dy/(du) xx (du)/dx`
Hence, find `d/dx[log(x^5 + 4)]`.
Find `dy/dx` if, y = `e^(5x^2 -2x + 4)`
Solve the following:
If y = `root5((3x^2 + 8x + 5)^4)`, find `dy/dx`
Find `dy/dx` if, y = `e^(5x^2-2x+4)`
If `y=root5((3x^2+8x+5)^4)`, find `dy/dx`
Find `"dy"/"dx"` if, y = `"e"^(5"x"^2 - 2"x" + 4)`
Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = 12 + 10`x + 25x^2`
Solve the following.
If `y=root(5)((3x^2 + 8x + 5)^4)`, find `dy/dx`
Solve the following:
If y = `root5((3x^2 + 8x + 5)^4)`, find `dy/(dx)`.
