Advertisements
Advertisements
प्रश्न
Find `"dy"/"dx"` if, x3 + x2y + xy2 + y3 = 81
Advertisements
उत्तर
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
संबंधित प्रश्न
Find `bb(dy/dx)` in the following:
x3 + x2y + xy2 + y3 = 81
Find the derivative of the function f defined by f (x) = mx + c at x = 0.
If \[\lim_{x \to c} \frac{f\left( x \right) - f\left( c \right)}{x - c}\] exists finitely, write the value of \[\lim_{x \to c} f\left( x \right)\]
Write the value of the derivative of f (x) = |x − 1| + |x − 3| at x = 2.
Find `"dy"/"dx"` ; if y = cos-1 `("2x" sqrt (1 - "x"^2))`
Find `(dy)/(dx) , "If" x^3 + y^2 + xy = 10`
Find `(dy)/(dx)` if `y = sin^-1(sqrt(1-x^2))`
If `sin^-1((x^5 - y^5)/(x^5 + y^5)) = pi/(6), "show that" "dy"/"dx" = x^4/(3y^4)`
If y = `sqrt(cosx + sqrt(cosx + sqrt(cosx + ... ∞)`, then show that `"dy"/"dx" = sinx/(1 - 2y)`.
Find `"dy"/"dx"` if x = a cot θ, y = b cosec θ
Find `"dy"/"dx"`, if : x = sinθ, y = tanθ
If x = `(t + 1)/(t - 1), y = (t - 1)/(t + 1), "then show that" y^2 + "dy"/"dx"` = 0.
Find `(d^2y)/(dx^2)` of the following : x = a cos θ, y = b sin θ at θ = `π/4`.
If y = x + tan x, show that `cos^2x.(d^2y)/(dx^2) - 2y + 2x` = 0.
If x = a sin t – b cos t, y = a cos t + b sin t, show that `(d^2y)/(dx^2) = -(x^2 + y^2)/(y^3)`.
Find the nth derivative of the following : (ax + b)m
Find the nth derivative of the following : eax+b
Find the nth derivative of the following : y = eax . cos (bx + c)
Find the nth derivative of the following:
y = e8x . cos (6x + 7)
Differentiate the following w.r.t. x : `sin[2tan^-1(sqrt((1 - x)/(1 + x)))]`
Choose the correct alternative.
If `"x"^4."y"^5 = ("x + y")^("m + 1")` then `"dy"/"dx" = "y"/"x"` then m = ?
Find `"dy"/"dx"` if x = `"e"^"3t", "y" = "e"^(sqrt"t")`.
`(dy)/(dx)` of `2x + 3y = sin x` is:-
If y = `sqrt(tan x + sqrt(tanx + sqrt(tanx + .... + ∞)`, then show that `dy/dx = (sec^2x)/(2y - 1)`.
Find `dy/dx` at x = 0.
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)`
If log(x + y) = log(xy) + a then show that, `dy/dx=(-y^2)/x^2`
