Advertisements
Advertisements
प्रश्न
(x2 + y2)2 = xy
Advertisements
उत्तर
Given that: (x2 + y2)2 = xy
⇒ x4 + y4 + 2x2y2 = xy
Differentiating both sides w.r.t. x
`"d"/"dx"(x^4) + "d"/"dx"(y^4) + 2*"d"/"dx"(x^2y^2) = "d"/"dx"(xy)`
⇒ `4x^3 + 4y^3 * "dy"/"dx" + 2[x^2*2y*"dy"/"dx" + y^2*2x] = x"dy"/"dx" + y*1`
⇒ `4x^3 + 4y^3 * "dy"/"dx" + 4x^2y * "dy"/"dx" + 4xy^2 = x "dy"/"dx" + y`
⇒ `4y^3 "dy"/"dx" + 4x^2y "dy"/"dx" - x "dy"/"dx" = y - 4x^3 - 4xy^2`
⇒ `(4y^3 + 4x^2y - x)"dy"/"dx" = y - 4x^3 - 4xy^2`
⇒ `"dy"/"dx" = (y - 4x^3 - 4xy^2)/(4y^3 + 4x^2y - x)`
Hence, `"dy"/"dx" = (y - 4x^3 - 4xy^2)/(4x^2y + 4x^2y - x)`.
APPEARS IN
संबंधित प्रश्न
If x = a sin t and `y = a (cost+logtan(t/2))` ,find `((d^2y)/(dx^2))`
If x = a cos θ + b sin θ, y = a sin θ − b cos θ, show that `y^2 (d^2y)/(dx^2)-xdy/dx+y=0`
Find the second order derivative of the function.
log x
If y = 5 cos x – 3 sin x, prove that `(d^2y)/(dx^2) + y = 0`.
If y = 3 cos (log x) + 4 sin (log x), show that x2y2 + xy1 + y = 0.
If y = Aemx + Benx, show that `(d^2y)/dx^2 - (m+ n) (dy)/dx + mny = 0`.
If y = 500e7x + 600e–7x, show that `(d^2y)/(dx^2)` = 49y.
Find `("d"^2"y")/"dx"^2`, if y = `"e"^"log x"`
Find `("d"^2"y")/"dx"^2`, if y = 2at, x = at2
If ax2 + 2hxy + by2 = 0, then show that `("d"^2"y")/"dx"^2` = 0
sec(x + y) = xy
If x sin (a + y) + sin a cos (a + y) = 0, prove that `"dy"/"dx" = (sin^2("a" + y))/sin"a"`
If x2 + y2 + sin y = 4, then the value of `(d^2y)/(dx^2)` at the point (–2, 0) is ______.
If y = `sqrt(ax + b)`, prove that `y((d^2y)/dx^2) + (dy/dx)^2` = 0.
If x = A cos 4t + B sin 4t, then `(d^2x)/(dt^2)` is equal to ______.
If x = a cos t and y = b sin t, then find `(d^2y)/(dx^2)`.
Find `(d^2y)/dx^2 if, y = e^((2x + 1))`
Find `(d^2y)/dx^2` if, `y = e^((2x + 1))`
Find `(d^2y)/dx^2` if, `y = e^((2x + 1))`
Find `(d^2y)/dx^2` if, y = `e^((2x + 1))`
Find `(d^2y)/dx^2` if, `y = e^((2x + 1))`
If y = 3 cos(log x) + 4 sin(log x), show that `x^2 (d^2y)/(dx^2) + x dy/dx + y = 0`
Find `(d^2y)/dx^2, "if" y = e^((2x+1))`
When is the second order derivative of \[y\] with respect to \[x\] defined?
If \[y=\mathrm{A}\sin x+\mathrm{B}\cos x\], what is \[\frac{dy}{dx}\]?
Which equation is equivalent to \[\frac{dy}{dx}=\frac{1}{\sqrt{1-x^2}}\] for \[y=\sin^{-1}x\]?
What equation is obtained after multiplying through by \[\sqrt{1-x^2}\] in the derivation for \[y=\sin^{-1}x\]?
