Advertisements
Advertisements
Question
If f'(4) = 5, f(4) = 3, g'(6) = 7 and R(x) = g[3 + f(x)] then R'(4) = ______
Options
35
12
`7/5`
105
Solution
35
RELATED QUESTIONS
If y = eax. cos bx, then prove that
`(d^2y)/(dx^2) - 2ady/dx + (a^2 + b^2)y` = 0
if `y = tan^2(log x^3)`, find `(dy)/(dx)`
Solve : `"dy"/"dx" = 1 - "xy" + "y" - "x"`
If y = log (cos ex) then find `"dy"/"dx".`
Find `"dy"/"dx"` if `sqrt(x) + sqrt(y) = sqrt(a)`
Find `"dy"/"dx"`If x3 + x2y + xy2 + y3 = 81
Find `"dy"/"dx"` if xey + yex = 1
Find the second order derivatives of the following : `2x^5 - 4x^3 - (2)/x^2 - 9`
Find the second order derivatives of the following : e2x . tan x
Find the second order derivatives of the following : xx
Find `"dy"/"dx"` if, y = log(log x)
Find `"dy"/"dx"` if, y = log(10x4 + 5x3 - 3x2 + 2)
Find `"dy"/"dx"` if, y = log(ax2 + bx + c)
Find `"dy"/"dx"` if, y = `5^(("x" + log"x"))`
Choose the correct alternative.
If y = `sqrt("x" + 1/"x")`, then `"dy"/"dx" = ?`
If y = 2x2 + 22 + a2, then `"dy"/"dx" = ?`
Fill in the Blank
If 3x2y + 3xy2 = 0, then `"dy"/"dx"` = ________
If `"x"^"m"*"y"^"n" = ("x + y")^("m + n")`, then `"dy"/"dx" = "______"/"x"`
The derivative of f(x) = ax, where a is constant is x.ax-1.
`d/dx(10^x) = x*10^(x - 1)`
Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = `(5x + 7)/(2x - 13)`
Differentiate `"e"^("4x" + 5)` with respect to 104x.
If y = cos−1 [sin (4x)], find `("d"y)/("d"x)`
If y = `1/sqrt(3x^2 - 2x - 1)`, then `("d"y)/("d"x)` = ?
Choose the correct alternative:
If y = `x^(sqrt(x))`, then `("d"y)/("d"x)` = ?
If y = x10, then `("d"y)/("d"x)` is ______
If y = x2, then `("d"^2y)/("d"x^2)` is ______
State whether the following statement is True or False:
If y = ex, then `("d"y)/("d"x)` = ex
Find `("d"y)/("d"x)`, if y = (6x3 – 3x2 – 9x)10
Find `("d"y)/("d"x)`, if y = `root(5)((3x^2 + 8x + 5)^4`
If u = x2 + y2 and x = s + 3t, y = 2s - t, then `(d^2u)/(ds^2)` = ______
If f(x) = `(x - 2)/(x + 2)`, then f(α x) = ______
If y = `x/"e"^(1 + x)`, then `("d"y)/("d"x)` = ______.
Derivative of ex sin x w.r.t. e-x cos x is ______.
Differentiate `sqrt(tansqrt(x))` w.r.t. 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 y = `sec^-1 ((sqrt(x) + 1)/(sqrt(x + 1))) + sin^-1((sqrt(x) - 1)/(sqrt(x) + 1))`, then `"dy"/"dx"` is equal to ______.
If `sqrt(1 - x^2) + sqrt(1 - y^2) = "a"(x - y)`, prove that `"dy"/"dx" = sqrt((1 - y^2)/(1 - x^2)`
If y = log (cos ex), then `"dy"/"dx"` is:
y = `cos sqrt(x)`
If ax2 + 2hxy + by2 = 0, then prove that `(d^2y)/(dx^2)` = 0.
Let x(t) = `2sqrt(2) cost sqrt(sin2t)` and y(t) = `2sqrt(2) sint sqrt(sin2t), t ∈ (0, π/2)`. Then `(1 + (dy/dx)^2)/((d^2y)/(dx^2)` at t = `π/4` is equal to ______.
If f(x) = `{{:(x^3 + 1",", x < 0),(x^2 + 1",", x ≥ 0):}`, g(x) = `{{:((x - 1)^(1//3)",", x < 1),((x - 1)^(1//2)",", x ≥ 1):}`, then (gof) (x) is equal to ______.
If y = em sin–1 x and (1 – x2) = Ay2, then A is equal to ______.
If y = 2x2 + a2 + 22 then `dy/dx` = ______.
If `d/dx` [f(x)] = ax+ b and f(0) = 0, then f(x) is equal to ______.
Find `dy/dx` if, `y=e^(5x^2-2x+4)`
Solve the following:
If`y=root(5)((3x^2+8x+5)^4),"find" (dy)/dx`
If `y = root5(3x^2 + 8x + 5)^4`, find `dy/dx`
Find `dy/dx` if, y = `e^(5x^2 - 2x + 4)`
Solve the following:
If y = `root5((3x^2 + 8x + 5)^4)`, find `dy/dx`
The differential equation of (x - a)2 + y2 = a2 is ______
Find `dy/dx` if, y = `e^(5 x^2 - 2x + 4)`
If y = `root5((3x^2 + 8x + 5)^4)`, find `dy/dx`
Find the rate of change of demand (x) of acommodity with respect to its price (y) if
`y = 12 + 10x + 25x^2`
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)]`.
Solve the following:
If y = `root5((3x^2 +8x+5)^4`,find `dy/dx`
If y = `sqrt((1 - x)/(1 + x))`, then `(1 - x^2) dy/dx + y` = ______.
If y = f(u) is a differentiable function of u and u = g(x) is a differentiate 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 `dy/dx` if y = log(x2 + 5)
Find `dy/dx` if, y = `e^(5x^2 - 2x + 4)`
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^(5x^2 - 2x +4)`
Find `dy/dx` if, `y=e^(5x^2-2x+4)`
If `y=root5((3x^2+8x+5)^4)`, find `dy/dx`
Solve the following:
If y = `root(5)((3"x"^2 + 8"x" + 5)^4)`, find `"dy"/"dx"`
Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = 12 + 10`x + 25x^2`
Find `(dy) / (dx)` if, `y = e ^ (5x^2 - 2x + 4)`
If `y = root{5}{(3x^2 + 8x + 5)^4}, "find" dy/dx`.
Find `dy/(dx)` if, y = `e^(5x^2 - 2x + 4)`
If `y = (x + sqrt(a^2 + x^2))^m`, prove that `(a^2 + x^2)(d^2y)/(dx^2) + xdy/dx - m^2y = 0`