Advertisements
Advertisements
Question
Find `"dy"/"dx"` if, x3 + x2y + xy2 + y3 = 81
Advertisements
Solution
x3 + x2y + xy2 + y3 = 81
Differentiating both sides w.r.t. x, we get
`3"x"^2 + "x"^2 "dy"/"dx" + "y" * "d"/"dx" ("x"^2) + "x"*"d"/"dx" ("y"^2) + "y"^2 * "d"/"dx" ("x") + 3"y"^2 * "dy"/"dx" = 0`
∴ `3"x"^2 + "x"^2 "dy"/"dx" + "y" * "2x" + "x" * "2y" "dy"/"dx" + "y"^2 + 3"y"^2 * "dy"/"dx" = 0`
∴ `(3"x"^2 + 2"xy" + "y"^2) + ("x"^2 + 2"xy" + 3"y"^2) "dy"/"dx" = 0`
∴ `("x"^2 + 2"xy" + 3"y"^2) "dy"/"dx" = - (3"x"^2 + 2"xy" + "y"^2)`
∴ `"dy"/"dx" = - (3"x"^2 + 2"xy" + "y"^2)/("x"^2 + 2"xy" + 3"y"^2)`
APPEARS IN
RELATED QUESTIONS
If y=eax ,show that `xdy/dx=ylogy`
if `x^y + y^x = a^b`then Find `dy/dx`
If f (x) = |x − 2| write whether f' (2) exists or not.
Find `(dy)/(dx) , "If" x^3 + y^2 + xy = 10`
If x = tan-1t and y = t3 , find `(dy)/(dx)`.
Find `"dy"/"dx"`, if : x = sinθ, y = tanθ
Find `"dy"/"dx"`, if : x = a(1 – cosθ), y = b(θ – sinθ)
Find `"dy"/"dx"` if : x = a cos3θ, y = a sin3θ at θ = `pi/(3)`
Find `dy/dx` if : x = 2 cos t + cos 2t, y = 2 sin t – sin 2t at t = `pi/(4)`
If y = `e^(mtan^-1x)`, show that `(1 + x^2)(d^2y)/(dx^2) + (2x - m)"dy"/"dx"` = 0.
If `sec^-1((7x^3 - 5y^3)/(7^3 + 5y^3)) = "m", "show" (d^2y)/(dx^2)` = 0.
Choose the correct option from the given alternatives :
If x = a(cosθ + θ sinθ), y = a(sinθ – θ cosθ), then `((d^2y)/dx^2)_(θ = pi/4)` = .........
Differentiate the following w.r.t. x : `sin[2tan^-1(sqrt((1 - x)/(1 + x)))]`
If sin y = x sin (a + y), then show that `"dy"/"dx" = (sin^2(a + y))/(sina)`.
If x = `e^(x/y)`, then show that `dy/dx = (x - y)/(xlogx)`
If log y = log (sin x) – x2, show that `(d^2y)/(dx^2) + 4x "dy"/"dx" + (4x^2 + 3)y` = 0.
If x= a cos θ, y = b sin θ, show that `a^2[y(d^2y)/(dx^2) + (dy/dx)^2] + b^2` = 0.
Find `"dy"/"dx"` if, x3 + y3 + 4x3y = 0
Find `"dy"/"dx"` if, yex + xey = 1
Choose the correct alternative.
If ax2 + 2hxy + by2 = 0 then `"dy"/"dx" = ?`
If `"x"^"a"*"y"^"b" = ("x + y")^("a + b")`, then show that `"dy"/"dx" = "y"/"x"`
If x2 + y2 = 1, then `(d^2x)/(dy^2)` = ______.
If `sqrt(x) + sqrt(y) = sqrt("a")`, then `("d"y)/("d"x)` is ______
y = `e^(x3)`
Find `(d^2y)/(dy^2)`, if y = e4x
Find `dy/dx if , x = e^(3t) , y = e^sqrtt`
If log (x+y) = log (xy) + a then show that, `dy/dx= (-y^2)/(x^2)`
Find `dy/dx` if, `x = e^(3t), y = e^sqrtt`
Find `dy/dx` if, `x = e^(3t), y = e^(sqrtt)`
