Advertisements
Advertisements
Question
Find `bb(dy/dx)` in the following:
sin2 x + cos2 y = 1
Advertisements
Solution
sin2 x + cos2 y = 1
Differentiating both sides with respect to x,
`d/dx sin^2 x + d/dx cos^2 y = d/dx (1)`
⇒ `2 sin x d/dx sin x + 2 cos y d/dx cos y = 0`
⇒ `2 sin x cos x + 2 cos y (- sin y) dy/dx = 0`
⇒ `2 sin x cos x - 2 cos y sin y dy/dx = 0`
⇒ `sin 2x - sin 2y dy/dx = 0`
∴ `dy/dx = (sin 2x) /(sin 2y)`
APPEARS IN
RELATED QUESTIONS
Find dy/dx if x sin y + y sin x = 0.
Find `bb(dy/dx)` in the following:
2x + 3y = sin y
Find `bb(dy/dx)` in the following:
`y = sin^(-1)((2x)/(1+x^2))`
Find the derivative of the function f defined by f (x) = mx + c at x = 0.
Find `dy/dx if x^3 + y^2 + xy = 7`
Differentiate tan-1 (cot 2x) w.r.t.x.
If x = tan-1t and y = t3 , find `(dy)/(dx)`.
Find `"dy"/"dx"` if x = at2, y = 2at.
Find `"dy"/"dx"`, if : x = `sqrt(a^2 + m^2), y = log(a^2 + m^2)`
Find `"dy"/"dx"`, if : x = a(1 – cosθ), y = b(θ – sinθ)
Find `"dy"/"dx"`, if : x = `(t + 1/t)^a, y = a^(t+1/t)`, where a > 0, a ≠ 1, t ≠ 0.
Find `"dy"/"dx"` if : x = cosec2θ, y = cot3θ at θ= `pi/(6)`
Differentiate `tan^-1((x)/(sqrt(1 - x^2))) w.r.t. sec^-1((1)/(2x^2 - 1))`.
Differentiate `tan^-1((sqrt(1 + x^2) - 1)/(x)) w.r.t tan^-1((2xsqrt(1 - x^2))/(1 - 2x^2))`.
Find `(d^2y)/(dx^2)` of the following : x = a cos θ, y = b sin θ at θ = `π/4`.
If x = at2 and y = 2at, then show that `xy(d^2y)/(dx^2) + a` = 0.
If y = x + tan x, show that `cos^2x.(d^2y)/(dx^2) - 2y + 2x` = 0.
If y = sin (m cos–1x), then show that `(1 - x^2)(d^2y)/(dx^2) - x"dy"/"dx" + m^2y` = 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)`.
Choose the correct option from the given alternatives :
If `xsqrt(y + 1) + ysqrt(x + 1) = 0 and x ≠ y, "then" "dy"/"dx"` = ........
If `xsqrt(1 - y^2) + ysqrt(1 - x^2)` = 1, then show that `"dy"/"dx" = -sqrt((1 - y^2)/(1 - x^2)`.
If sin y = x sin (a + y), then show that `"dy"/"dx" = (sin^2(a + y))/(sina)`.
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, sqrt"x" + sqrt"y" = sqrt"a"`
Find `"dy"/"dx"` if, x3 + x2y + xy2 + y3 = 81
Find `"dy"/"dx"` if, `"x"^"y" = "e"^("x - y")`
Solve the following:
If `"e"^"x" + "e"^"y" = "e"^((x + y))` then show that, `"dy"/"dx" = - "e"^"y - x"`.
If `x^7 * y^9 = (x + y)^16`, then show that `dy/dx = y/x`
If x2 + y2 = t + `1/"t"` and x4 + y4 = t2 + `1/"t"^2` then `("d"y)/("d"x)` = ______
If x = a t4 y = 2a t2 then `("d"y)/("d"x)` = ______
`(dy)/(dx)` of `2x + 3y = sin x` is:-
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^sqrt t`
Find `dy/dx` if, `x = e^(3t), y = e^(sqrtt)`
Find `dy/(dx) "if" , x = e^(3t), y = e^sqrtt`.
