Advertisements
Advertisements
प्रश्न
If `"x"^(5/3) . "y"^(2/3) = ("x + y")^(7/3)` , the show that `"dy"/"dx" = "y"/"x"`
उत्तर
`"x"^(5/3) . "y"^(2/3) = ("x + y")^(7/3)`
Taking logarithm of both the sides , we get
`5/3 "log x" + 2/3 "log y" = 7/3 "log (x + y)"`
Differentiating both sides w.r.t. x,
`5/3 . 1/"x" + 2/3 . 1/"y" "dy"/"dx" = 7/3 . 1/("x + y") [1 + "dy"/"dx"]`
`therefore 2/"3y" "dy"/"dx" - 7/(3 ("x + y")) "dy"/"dx" = 7/(3 ("x + y")) - 5/"3x"`
`therefore [2/"3y" - 7/(3 ("x + y"))] "dy"/"dx" = (7"x" - 5("x + y"))/("3x"("x + y"))`
`therefore [(2("x + y") - "7y")/("3y" ("x + y"))] "dy"/"dx" = (7"x" - 5("x + y"))/("3x"("x + y"))`
`therefore ("2x" - "5y")/"y" "dy"/"dx" = (2"x" - 5"y")/"x"`
`therefore "dy"/"dx" = "y"/"x"`
APPEARS IN
संबंधित प्रश्न
Differentiate the following function with respect to x: `(log x)^x+x^(logx)`
If `y=log[x+sqrt(x^2+a^2)] ` show that `(x^2+a^2)(d^2y)/(dx^2)+xdy/dx=0`
Differentiate the function with respect to x.
`sqrt(((x-1)(x-2))/((x-3)(x-4)(x-5)))`
Differentiate the function with respect to x.
`(x + 1/x)^x + x^((1+1/x))`
If `y = e^(acos^(-1)x)`, -1 <= x <= 1 show that `(1- x^2) (d^2y)/(dx^2) -x dy/dx - a^2y = 0`
If `y = sin^-1 x + cos^-1 x , "find" dy/dx`
Find `"dy"/"dx"` , if `"y" = "x"^("e"^"x")`
xy = ex-y, then show that `"dy"/"dx" = ("log x")/("1 + log x")^2`
`"If" y = sqrt(logx + sqrt(log x + sqrt(log x + ... ∞))), "then show that" dy/dx = (1)/(x(2y - 1).`
If x = 2cos4(t + 3), y = 3sin4(t + 3), show that `"dy"/"dx" = -sqrt((3y)/(2x)`.
Differentiate 3x w.r.t. logx3.
Find the second order derivatives of the following : x3.logx
If y = log (log 2x), show that xy2 + y1 (1 + xy1) = 0.
Choose the correct option from the given alternatives :
If xy = yx, then `"dy"/"dx"` = ..........
If y = log [cos(x5)] then find `("d"y)/("d"x)`
If y = 5x. x5. xx. 55 , find `("d"y)/("d"x)`
If y = `{f(x)}^{phi(x)}`, then `dy/dx` is ______
If `"f" ("x") = sqrt (1 + "cos"^2 ("x"^2)), "then the value of f'" (sqrtpi/2)` is ____________.
If y = `(1 + 1/x)^x` then `(2sqrt(y_2(2) + 1/8))/((log 3/2 - 1/3))` is equal to ______.
