Advertisements
Advertisements
प्रश्न
Find `dy/dx if x^2y^2 - tan^-1(sqrt(x^2 + y^2)) = cot^-1(sqrt(x^2 + y^2))`
उत्तर
`x^2y^2 - tan^-1(sqrt(x^2 + y^2)) = cot^-1(sqrt(x^2 + y^2))`
∴ `x^2y^2 = tan^-1(sqrt(x^2 + y^2)) + cot^-1(sqrt(x^2 + y^2))`
∴ `x^2y^2 = π/2 ...[∵ tan^-1 x + cot^-1 x = π/2]`
Differentiating both sides w.r.t. x, we get,
`x^2.d/dx(y^2) + y^2.d/dx(x^2) = 0`
∴ `x^2 × 2y dy/dx + y^2 × 2x = 0`
∴ `2x^2y dy/dx = – 2xy^2`
∴ `x dy/dx = – y`
∴ `dy/dx = -y/x`.
APPEARS IN
संबंधित प्रश्न
Solve the following differential equation:
x2 dy + (xy + y2) dx = 0, when x = 1 and y = 1
Find `"dy"/"dx"` if `sqrt(x) + sqrt(y) = sqrt(a)`
Find the second order derivatives of the following : `2x^5 - 4x^3 - (2)/x^2 - 9`
Find `"dy"/"dx"` if, y = `sqrt("x" + 1/"x")`
Find `"dy"/"dx"` if, y = `root(3)("a"^2 + "x"^2)`
Find `"dy"/"dx"` if, y = log(10x4 + 5x3 - 3x2 + 2)
Find `"dy"/"dx"` if, y = log(ax2 + bx + c)
Find `"dy"/"dx"` if, y = `"a"^((1 + log "x"))`
Find `"dy"/"dx"` if, y = `5^(("x" + log"x"))`
Choose the correct alternative.
If y = (5x3 - 4x2 - 8x)9, then `"dy"/"dx"` =
If y = 2x2 + 22 + a2, 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.
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 the rate of change of demand (x) of a commodity with respect to its price (y) if y = `(5x + 7)/(2x - 13)`
Find `"dy"/"dx"`, if y = `2^("x"^"x")`.
If f'(4) = 5, f(4) = 3, g'(6) = 7 and R(x) = g[3 + f(x)] then R'(4) = ______
If y = cos−1 [sin (4x)], find `("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 y = `1/sqrt(3x^2 - 2x - 1)`, then `("d"y)/("d"x)` = ?
Choose the correct alternative:
If y = `root(3)((3x^2 + 8x - 6)^5`, then `("d"y)/("d"x)` = ?
If y = (5x3 – 4x2 – 8x)9, then `("d"y)/("d"x)` is ______
If y = `("e")^((2x + 5))`, then `("d"y)/("d"x)` is ______
State whether the following statement is True or False:
If y = ex, then `("d"^2y)/("d"x^2)` = ex
Find `("d"y)/("d"x)`, if y = (6x3 – 3x2 – 9x)10
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) = ______
Derivative of ex sin x w.r.t. e-x cos x is ______.
If y = (sin x2)2, then `("d"y)/("d"x)` is equal to ______.
`"d"/("d"x) [sin(1 - x^2)]^2` = ______.
If y = `(cos x)^((cosx)^((cosx))`, then `("d")/("d"x)` = ______.
Given f(x) = `1/(x - 1)`. Find the points of discontinuity of the composite function y = f[f(x)]
If f(x) = |cos x – sinx|, find `"f'"(pi/6)`
If `sqrt(1 - x^2) + sqrt(1 - y^2) = "a"(x - y)`, prove that `"dy"/"dx" = sqrt((1 - y^2)/(1 - x^2)`
Differentiate the function from over no 15 to 20 sin (x2 + 5)
y = cos (sin x)
y = sin (ax+ b)
y = `sec (tan sqrt(x))`
If ax2 + 2hxy + by2 = 0, then prove that `(d^2y)/(dx^2)` = 0.
Let f(x) = log x + x3 and let g(x) be the inverse of f(x), then |64g"(1)| 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` = ______.
Find `"dy"/"dx" if, e ^(5"x"^2- 2"X"+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`
Solve the following:
If y = `root5((3x^2 + 8x + 5)^4)`, find `dy/dx`
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)]`.
Find `dy/dx` if, y = `e^(5x^2-2x+4)`
Solve the following:
If y = `root5((3x^2 +8x+5)^4`,find `dy/dx`
If y = `log((x + sqrt(x^2 + a^2))/(sqrt(x^2 + a^2) - x))`, 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)((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"^(5"x"^2 - 2"x" + 4)`
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)`
Find `dy/(dx)` if, y = `e^(5x^2 - 2x + 4)`
