Advertisements
Advertisements
Question
Find `"dy"/"dx"` for the following function.
x2 – xy + y2 = 1
Solution
x2 – xy + y2 = 1
Differentiating both side with respect to x,
`"d"/"dx" (x^2) - "d"/"dx" (xy) + "d"/"dx" (y^2) = "d"/"dx"(7)`
`2x - [x "d"/"dx" (y) + y "d"/"dx" (x)] + 2y "dy"/"dx" = 0`
`2x - [x "dy"/"dx" + y * 1] + 2y "dy"/"dx" = 0`
`2x - x"dy"/"dx" - y + 2y "dy"/"dx"` = 0
`"dy"/"dx" [2x - x] = y - 2x`
`"dy"/"dx" = (y - 2x)/(2y - x)`
APPEARS IN
RELATED QUESTIONS
Differentiate the following with respect to x.
(x2 – 3x + 2) (x + 1)
Differentiate the following with respect to x.
cos2 x
Differentiate the following with respect to x.
`1/sqrt(1 + x^2)`
Find `"dy"/"dx"` for the following function
xy – tan(xy)
Differentiate the following with respect to x.
(sin x)tan x
If xm . yn = (x + y)m+n, then show that `"dy"/"dx" = y/x`
Find y2 for the following function:
y = log x + ax
Find y2 for the following function:
x = a cosθ, y = a sinθ
If y = 500e7x + 600e-7x, then show that y2 – 49y = 0.
If xy2 = 1, then prove that `2 "dy"/"dx" + y^3`= 0
