Advertisements
Advertisements
Question
Choose the correct alternative.
If ax2 + 2hxy + by2 = 0 then `"dy"/"dx" = ?`
Options
`(("ax" + "hx"))/(("hx" + "by"))`
`(-("ax" + "hx"))/(("hx" + "by"))`
`(("ax" - "hx"))/(("hx" + "by"))`
`(("2ax" + "hy"))/(("hx" + "3by"))`
Advertisements
Solution
`(-("ax" + "hx"))/(("hx" + "by"))`
Explanation:
ax2 + 2hxy + by2 = 0
Differentiating both sides w.r.t.x, we get
`"a"(2"x") + "2h" * "d"/"dx" ("xy") + "b"("2y") "dy"/"dx" = 0`
∴ 2ax + 2h `["x" * "dy"/"dx" + "y"(1)] + 2"by" "dy"/"dx" = 0`
∴ 2ax + 2hx `"dy"/"dx"` + 2hy + 2by`"dy"/"dx"` = 0
∴ 2`"dy"/"dx"`(hx + by) = - 2ax - 2hy
∴ 2`"dy"/"dx" = (-2("ax" + "hy"))/(("hx" + "by"))`
∴ `"dy"/"dx" = (-("ax" + "hx"))/(("hx" + "by"))`
APPEARS IN
RELATED QUESTIONS
If y=eax ,show that `xdy/dx=ylogy`
Find `bb(dy/dx)` in the following:
`y = sin^(-1)((2x)/(1+x^2))`
if `(x^2 + y^2)^2 = xy` find `(dy)/(dx)`
If for the function
\[\Phi \left( x \right) = \lambda x^2 + 7x - 4, \Phi'\left( 5 \right) = 97, \text { find } \lambda .\]
If f (x) = |x − 2| write whether f' (2) exists or not.
Discuss extreme values of the function f(x) = x.logx
Find `"dy"/"dx"` if : x = t2 + t + 1, y = `sin((pit)/2) + cos((pit)/2) "at" t = 1`
Find `dy/dx` if : x = 2 cos t + cos 2t, y = 2 sin t – sin 2t at t = `pi/(4)`
Find `"dy"/"dx"` if : x = t + 2sin (πt), y = 3t – cos (πt) at t = `(1)/(2)`
Differentiate `sin^-1((2x)/(1 + x^2))w.r.t. cos^-1((1 - x^2)/(1 + x^2))`
If y = x + tan x, show that `cos^2x.(d^2y)/(dx^2) - 2y + 2x` = 0.
If 2y = `sqrt(x + 1) + sqrt(x - 1)`, show that 4(x2 – 1)y2 + 4xy1 – y = 0.
Find the nth derivative of the following : cos x
If y `tan^-1(sqrt((a - x)/(a + x)))`, where – a < x < a, then `"dy"/"dx"` = .........
If sin y = x sin (a + y), then show that `"dy"/"dx" = (sin^2(a + y))/(sina)`.
If x = `e^(x/y)`, then show that `dy/dx = (x - y)/(xlogx)`
If log y = log (sin x) – x2, show that `(d^2y)/(dx^2) + 4x "dy"/"dx" + (4x^2 + 3)y` = 0.
If log (x + y) = log (xy) + a then show that, `"dy"/"dx" = (- "y"^2)/"x"^2`.
Choose the correct alternative.
If y = 5x . x5, then `"dy"/"dx" = ?`
Choose the correct alternative.
If x = `("e"^"t" + "e"^-"t")/2, "y" = ("e"^"t" - "e"^-"t")/2` then `"dy"/"dx"` = ?
If x = sin θ, y = tan θ, then find `("d"y)/("d"x)`.
Differentiate w.r.t x (over no. 24 and 25) `e^x/sin x`
Find `(dy)/(dx)` if x + sin(x + y) = y – cos(x – y)
If y = y(x) is an implicit function of x such that loge(x + y) = 4xy, then `(d^2y)/(dx^2)` at x = 0 is equal to ______.
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`
Find `dy/dx"if", x= e^(3t), y=e^sqrtt`
