Advertisements
Advertisements
Question
If x2 + y2 = t + `1/"t"` and x4 + y4 = t2 + `1/"t"^2` then `("d"y)/("d"x)` = ______
Options
`x/(2y)`
`(-y)/x`
`(-x)/(2y)`
`y/x`
Advertisements
Solution
`(-y)/x`
APPEARS IN
RELATED QUESTIONS
If xpyq = (x + y)p+q then Prove that `dy/dx = y/x`
Find `bb(dy/dx)` in the following:
2x + 3y = sin x
Find `bb(dy/dx)` in the following:
2x + 3y = sin y
Find `bb(dy/dx)` in the following:
x2 + xy + y2 = 100
Find `bb(dy/dx)` in the following:
x3 + x2y + xy2 + y3 = 81
Find `bb(dy/dx)` in the following:
sin2 x + cos2 y = 1
if `(x^2 + y^2)^2 = xy` find `(dy)/(dx)`
Show that the derivative of the function f given by
Find the derivative of the function f defined by f (x) = mx + c at x = 0.
Write the derivative of f (x) = |x|3 at x = 0.
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
Differentiate tan-1 (cot 2x) w.r.t.x.
If `sin^-1((x^5 - y^5)/(x^5 + y^5)) = pi/(6), "show that" "dy"/"dx" = x^4/(3y^4)`
Find `"dy"/"dx"`, if : x = a(1 – cosθ), y = b(θ – sinθ)
Find `"dy"/"dx"`, if : `x = cos^-1(4t^3 - 3t), y = tan^-1(sqrt(1 - t^2)/t)`.
Differentiate `sin^-1((2x)/(1 + x^2))w.r.t. cos^-1((1 - x^2)/(1 + x^2))`
Find `(d^2y)/(dx^2)` of the following : x = a(θ – sin θ), y = a(1 – cos θ)
If y = x + tan x, show that `cos^2x.(d^2y)/(dx^2) - 2y + 2x` = 0.
If x2 + 6xy + y2 = 10, show that `(d^2y)/(dx^2) = (80)/(3x + y)^3`.
Find the nth derivative of the following:
`(1)/x`
Find the nth derivative of the following : apx+q
Find the nth derivative of the following : cos (3 – 2x)
Find the nth derivative of the following : `(1)/(3x - 5)`
Choose the correct option from the given alternatives :
If f(x) = `sin^-1((4^(x + 1/2))/(1 + 2^(4x)))`, which of the following is not the derivative of f(x)?
Choose the correct option from the given alternatives :
If y = sin (2sin–1 x), then dx = ........
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)` = .........
If x sin (a + y) + sin a . cos (a + y) = 0, then show that `"dy"/"dx" = (sin^2(a + y))/(sina)`.
If x = `e^(x/y)`, then show that `dy/dx = (x - y)/(xlogx)`
If x= a cos θ, y = b sin θ, show that `a^2[y(d^2y)/(dx^2) + (dy/dx)^2] + b^2` = 0.
If y = Aemx + Benx, show that y2 – (m + n)y1 + mny = 0.
Find `"dy"/"dx"` if, `"x"^"y" = "e"^("x - y")`
Choose the correct alternative.
If ax2 + 2hxy + by2 = 0 then `"dy"/"dx" = ?`
If x2 + y2 = 1, then `(d^2x)/(dy^2)` = ______.
If y = `sqrt(tansqrt(x)`, find `("d"y)/("d"x)`.
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)
Let y = y(x) be a function of x satisfying `ysqrt(1 - x^2) = k - xsqrt(1 - y^2)` where k is a constant and `y(1/2) = -1/4`. Then `(dy)/(dx)` at x = `1/2`, is equal to ______.
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 y = `(x + sqrt(x^2 - 1))^m`, show that `(x^2 - 1)(d^2y)/(dx^2) + xdy/dx` = m2y
Find `dy / dx` if, x = `e^(3t), y = e^sqrt t`
Find `dy/dx` if, `x = e^(3t), y = e^sqrtt`
Find `dy/dx` if, `x = e^(3t), y = e^(sqrtt)`
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`
