Advertisements
Advertisements
प्रश्न
Solve : `"dy"/"dx" = 1 - "xy" + "y" - "x"`
उत्तर
`"dy"/"dx" = 1 - "xy" + "y" - "x"`
`"dy"/"dx" = (1 + "y") - "x" (1 + "y")`
`"dy"/"dx" = (1 + "y") (1 - "x")`
`"dy"/(1 + "y") = (1 - "x")"dx"`
Integrating bothe sides, we obtain
`int"dy"/(1 + "y") = int (1 - "x")"dx"`
log |1 + y| `= "x" - "x"^2/2 + "C"`
APPEARS IN
संबंधित प्रश्न
if `y = tan^2(log x^3)`, find `(dy)/(dx)`
Find `"dy"/"dx"` if ex+y = cos(x – y)
Find the second order derivatives of the following : `2x^5 - 4x^3 - (2)/x^2 - 9`
Find the second order derivatives of the following : xx
Find `"dy"/"dx"` if, y = `root(3)("a"^2 + "x"^2)`
Find `"dy"/"dx"` if, y = log(log x)
Find `"dy"/"dx"` if, y = log(ax2 + bx + c)
If `"x"^"m"*"y"^"n" = ("x + y")^("m + n")`, then `"dy"/"dx" = "______"/"x"`
State whether the following is True or False:
The derivative of polynomial is polynomial.
Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = `(5x + 7)/(2x - 13)`
If y = sec (tan−1x) then `("d"y)/("d"x)` at x = 1 is ______.
If sin−1(x3 + y3) = a then `("d"y)/("d"x)` = ______
If y = `1/sqrt(3x^2 - 2x - 1)`, then `("d"y)/("d"x)` = ?
If y = `("e")^((2x + 5))`, then `("d"y)/("d"x)` is ______
State whether the following statement is True or False:
If y = ex, then `("d"y)/("d"x)` = ex
If y = `x/"e"^(1 + x)`, then `("d"y)/("d"x)` = ______.
If y = `sin^-1 {xsqrt(1 - x) - sqrt(x) sqrt(1 - x^2)}` and 0 < x < 1, then find `("d"y)/(dx)`
Let f(x) = log x + x3 and let g(x) be the inverse of f(x), then |64g"(1)| is equal to ______.
If `d/dx` [f(x)] = ax+ b and f(0) = 0, then f(x) is equal to ______.
If `y = root5(3x^2 + 8x + 5)^4`, find `dy/dx`
The differential equation of (x - a)2 + y2 = a2 is ______
If x = Φ(t) is a differentiable function of t, then prove that:
`int f(x)dx = int f[Φ(t)]*Φ^'(t)dt`
Hence, find `int(logx)^n/x dx`.
If y = `sqrt((1 - x)/(1 + x))`, then `(1 - x^2) dy/dx + y` = ______.
If y = `root5((3x^2+8x+5)^4)`, find `dy/dx`
Find `dy/dx` if, `y=e^(5x^2-2x+4)`
Solve the following:
If y = `root(5)((3"x"^2 + 8"x" + 5)^4)`, find `"dy"/"dx"`
Find `dy/dx` if, `y = e^(5x^2 - 2x+4)`
