Advertisements
Advertisements
प्रश्न
If y = cos−1 [sin (4x)], find `("d"y)/("d"x)`
उत्तर
y = cos−1 [sin (4x)]
= `cos^-1 [cos(pi/2 - 4^x)]`
= y = `pi/2 - 4^x`
Differentiating w.r.t. x, we get
`("d"y)/("d"x) = "d"/("d"x)(pi/2 - 4^x)`
= 0 – 4x log 4
= – 4x log 4
APPEARS IN
संबंधित प्रश्न
If y = eax. cos bx, then prove that
`(d^2y)/(dx^2) - 2ady/dx + (a^2 + b^2)y` = 0
Solve : `"dy"/"dx" = 1 - "xy" + "y" - "x"`
Solve the following differential equation:
x2 dy + (xy + y2) dx = 0, when x = 1 and y = 1
Find the second order derivatives of the following : e2x . tan x
Find the second order derivatives of the following : e4x. cos 5x
Find `"dy"/"dx"` if, y = `"e"^(5"x"^2 - 2"x" + 4)`
Find `"dy"/"dx"` if, y = `5^(("x" + log"x"))`
Choose the correct alternative.
If y = `sqrt("x" + 1/"x")`, then `"dy"/"dx" = ?`
Fill in the Blank
If 3x2y + 3xy2 = 0, then `"dy"/"dx"` = ________
The derivative of f(x) = ax, where a is constant is x.ax-1.
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"`
Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = 25 + 30x – x2.
Find `"dy"/"dx"`, if y = xx.
Differentiate `"e"^("4x" + 5)` with respect to 104x.
If sin−1(x3 + y3) = a then `("d"y)/("d"x)` = ______
If 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 `("d"y)/("d"x) = ("d"y)/("d"u)*("d"u)/("d"x)`. Hence find `("d"y)/("d"x)` if y = sin2x
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
If y = (5x3 – 4x2 – 8x)9, then `("d"y)/("d"x)` is ______
If y = `("e")^((2x + 5))`, then `("d"y)/("d"x)` is ______
Find `("d"y)/("d"x)`, if y = (6x3 – 3x2 – 9x)10
Find `("d"^2y)/("d"x^2)`, if y = `"e"^((2x + 1))`
Find `("d"y)/("d"x)`, if y = `root(5)((3x^2 + 8x + 5)^4`
y = (6x4 – 5x3 + 2x + 3)6, find `("d"y)/("d"x)`
Solution: Given,
y = (6x4 – 5x3 + 2x + 3)6
Let u = `[6x^4 - 5x^3 + square + 3]`
∴ y = `"u"^square`
∴ `("d"y)/"du"` = 6u6–1
∴ `("d"y)/"du"` = 6( )5
and `"du"/("d"x) = 24x^3 - 15(square) + 2`
By chain rule,
`("d"y)/("d"x) = ("d"y)/square xx square/("d"x)`
∴ `("d"y)/("d"x) = 6(6x^4 - 5x^3 + 2x + 3)^square xx (24x^3 - 15x^2 + square)`
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 = (sin x2)2, then `("d"y)/("d"x)` is equal to ______.
If ex + ey = ex+y , prove that `("d"y)/("d"x) = -"e"^(y - x)`
If y = `sin^-1 {xsqrt(1 - x) - sqrt(x) sqrt(1 - x^2)}` and 0 < x < 1, then find `("d"y)/(dx)`
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)`
y = sin (ax+ b)
y = `sec (tan sqrt(x))`
Let f(x) = log x + x3 and let g(x) be the inverse of f(x), then |64g"(1)| is equal to ______.
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 ______.
Let f(x) = x | x | and g(x) = sin x
Statement I gof is differentiable at x = 0 and its derivative is continuous at that point.
Statement II gof is twice differentiable at x = 0.
Find `"dy"/"dx" if, e ^(5"x"^2- 2"X"+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"`
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`
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 `dy/dx` if ,
`x= e^(3t) , y = e^(4t+5)`
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 = `tan^-1((6x - 7)/(6 + 7x))`, then `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 `dy/dx` if, `y = e^(5x^2 - 2x+4)`
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)`
Solve the following:
If y = `root5((3x^2 + 8x + 5)^4)`, find `dy/(dx)`.
