Advertisements
Advertisements
Question
Find `"dy"/"dx"` for the following function.
x3 + y3 + 3axy = 1
Advertisements
Solution
x3 + y3 + 3axy = 1
Differentiating both sides with respect to x,
`3x^2 + 3y^2 "dy"/"dx" + 3"a" (x "dy"/"dx" + y * 1) = 0`
`3[x^2 + y^2 "dy"/"dx" + "a"x "dy"/"dx" + "a"y] = 0`
`x^2 + y^2 "dy"/"dx" + "a"x "dy"/"dx" + "a"y = 0`
`"dy"/"dx" [y^2 + "a"x] = - x^2 - "a"y`
`"dy"/"dx" = (- x^2 - "a"y)/(y^2 + "a"x)`
`= - (x^2 + "a"y)/(y^2 + "a"x)`
`= - [(x^2 + "a"y)/(y^2 + "a"x)]`
APPEARS IN
RELATED QUESTIONS
Differentiate the following with respect to x.
x3 ex
Differentiate the following with respect to x.
`(sqrtx + 1/sqrtx)^2`
Differentiate the following with respect to x.
`e^x/(1 + x)`
Differentiate the following with respect to x.
sin x cos x
Differentiate the following with respect to x.
(ax2 + bx + c)n
Differentiate the following with respect to x.
xsin x
Differentiate the following with respect to x.
(sin x)tan x
Find `"dy"/"dx"` of the following function:
x = a cos3θ, y = a sin3θ
If y = `(x + sqrt(1 + x^2))^m`, then show that (1 + x2) y2 + xy1 – m2y = 0
If xy2 = 1, then prove that `2 "dy"/"dx" + y^3`= 0
