Advertisements
Advertisements
प्रश्न
Find `bb(dy/dx)` in the following:
x3 + x2y + xy2 + y3 = 81
Advertisements
उत्तर
x3 + x2y + xy2 + y3 = 81
Differentiating both sides with respect to x,
`d/dx (x^3) + {x^2 dy/dx + y d/dx (x^2)} + {x dy/dx (y^2) + y^2 d/dx (x)} + d/dx (y^3) = d/dx (81)`
⇒ `3 x^2 + x^2 dy/dx + y xx 2x + x xx 2y dy/dx + y^2 xx 1 + 3y^2 dy/d" = 0`
⇒ `x^2 dy/dx + x xx 2y dy/dx + 3y^2 dy/dx = -(3 x^2 + 2xy + y^2)`
∴ `dy/dx = (- (3 x^2 + 2xy + y^2))/( x^2 + 2xy + 3y^2)`
APPEARS IN
संबंधित प्रश्न
If y=eax ,show that `xdy/dx=ylogy`
If xpyq = (x + y)p+q then Prove that `dy/dx = y/x`
Find dy/dx if x sin y + y sin x = 0.
Find `bb(dy/dx)` in the following:
xy + y2 = tan x + y
Find `bb(dy/dx)` in the following:
sin2 y + cos xy = k
if `(x^2 + y^2)^2 = xy` find `(dy)/(dx)`
Let \[f\left( x \right)\begin{cases}a x^2 + 1, & x > 1 \\ x + 1/2, & x \leq 1\end{cases}\] . Then, f (x) is derivable at x = 1, if
Find `dy/dx if x^3 + y^2 + xy = 7`
Find `"dy"/"dx"` ; if x = sin3θ , y = cos3θ
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)`.
If x = cos t, y = emt, show that `(1 - x^2)(d^2y)/(dx^2) - x"dy"/"dx" - m^2y` = 0.
Find the nth derivative of the following:
`(1)/x`
Find the nth derivative of the following : sin (ax + 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)
Choose the correct option from the given alternatives :
Let `f(1) = 3, f'(1) = -(1)/(3), g(1) = -4 and g'(1) =-(8)/(3).` The derivative of `sqrt([f(x)]^2 + [g(x)]^2` w.r.t. x at x = 1 is
Differentiate the following w.r.t. x : `tan^-1((sqrt(x)(3 - x))/(1 - 3x))`
Differentiate the following w.r.t. x : `cos^-1((sqrt(1 + x) - sqrt(1 - x))/2)`
Differentiate the following w.r.t. x:
`tan^-1(x/(1 + 6x^2)) + cot^-1((1 - 10x^2)/(7x))`
If log y = log (sin x) – x2, show that `(d^2y)/(dx^2) + 4x "dy"/"dx" + (4x^2 + 3)y` = 0.
Find `"dy"/"dx"` if, x3 + x2y + xy2 + y3 = 81
Choose the correct alternative.
If ax2 + 2hxy + by2 = 0 then `"dy"/"dx" = ?`
Choose the correct alternative.
If `"x"^4."y"^5 = ("x + y")^("m + 1")` then `"dy"/"dx" = "y"/"x"` then m = ?
Choose the correct alternative.
If x = `("e"^"t" + "e"^-"t")/2, "y" = ("e"^"t" - "e"^-"t")/2` then `"dy"/"dx"` = ?
Find `"dy"/"dx"` if x = `"e"^"3t", "y" = "e"^(sqrt"t")`.
If x = sin θ, y = tan θ, then find `("d"y)/("d"x)`.
If `sqrt(x) + sqrt(y) = sqrt("a")`, then `("d"y)/("d"x)` is ______
`(dy)/(dx)` of `2x + 3y = sin x` is:-
Find `(dy)/(dx)`, if `y = sin^-1 ((2x)/(1 + x^2))`
y = `e^(x3)`
If y = `e^(m tan^-1x)` then show that `(1 + x^2) (d^2y)/(dx^2) + (2x - m) (dy)/(dx)` = 0
Find `(dy)/(dx)` if x + sin(x + y) = y – cos(x – y)
Find `(d^2y)/(dy^2)`, if y = e4x
If 2x + 2y = 2x+y, then `(dy)/(dx)` is equal to ______.
If log(x+y) = log(xy) + a then show that, `dy/dx = (-y^2)/x^2`
Find `dy/dx` if, x = e3t, y = `e^sqrtt`
Find `dy/dx` if, `x = e^(3t), y = e^sqrtt`
Find `dy/dx"if", x= e^(3t), y=e^sqrtt`
