हिंदी

If `Xpowery + Ypowerx = Apowerb`Then Find `Dybydx` - Mathematics

Advertisements
Advertisements

प्रश्न

if `x^y + y^x = a^b`then Find `dy/dx`

उत्तर

Given that,

`x^y + y^x = a^b`
=> `e^(ylogx) + e^(xlogy) = a^b`

On differentiating both sides with respect to x, we get

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
2016-2017 (March) All India Set 1

संबंधित प्रश्न

If  \[f\left( x \right) = x^3 + 7 x^2 + 8x - 9\] 

, find f'(4).


Find `(dy)/(dx)` if `y = sin^-1(sqrt(1-x^2))`


If x = tan-1t and y = t3 , find `(dy)/(dx)`.


If y = `sqrt(cosx + sqrt(cosx + sqrt(cosx + ... ∞)`, then show that `"dy"/"dx" = sinx/(1 - 2y)`.


Find `"dy"/"dx"`, if : x = sinθ, y = tanθ


Find `"dy"/"dx"`, if : `x = cos^-1((2t)/(1 + t^2)), y = sec^-1(sqrt(1 + t^2))`


Find `"dy"/"dx"` if : x = a cos3θ, y = a sin3θ at θ = `pi/(3)`


If y = `e^(mtan^-1x)`, show that `(1 + x^2)(d^2y)/(dx^2) + (2x - m)"dy"/"dx"` = 0.


If x2 + 6xy + y2 = 10, show that `(d^2y)/(dx^2) = (80)/(3x + y)^3`.


Find the nth derivative of the following : `(1)/(3x - 5)`


Choose the correct option from the given alternatives :

If y = sin (2sin–1 x), then dx = ........


Choose the correct option from the given alternatives :

If y = `tan^-1(x/(1 + sqrt(1 - x^2))) + sin[2tan^-1(sqrt((1 - x)/(1 + x)))] "then" "dy"/"dx"` = ...........


Choose the correct option from the given alternatives :

If x = a(cosθ + θ sinθ), y = a(sinθ – θ cosθ), then `((d^2y)/dx^2)_(θ = pi/4)` = .........


Differentiate the following w.r.t. x : `tan^-1[sqrt((sqrt(1 + x^2) + x)/(sqrt(1 + x^2) - x))]`


If `x = e^(x/y)`, then show that `"dy"/"dx" = (x - y)/(xlogx)`


If y = Aemx + Benx, show that y2 – (m + n)y1 + mny = 0.


Find `"dy"/"dx"` if, x3 + y3 + 4x3y = 0 


Find `"dy"/"dx"` if, xy = log (xy)


Choose the correct alternative.

If y = 5x . x5, then `"dy"/"dx" = ?` 


Choose the correct alternative.

If ax2 + 2hxy + by2 = 0 then `"dy"/"dx" = ?` 


If y = `("x" + sqrt("x"^2 - 1))^"m"`, then `("x"^2 - 1) "dy"/"dx"` = ______.


If `"x"^"a"*"y"^"b" = ("x + y")^("a + b")`, then show that `"dy"/"dx" = "y"/"x"`


Find `"dy"/"dx"` if x = `"e"^"3t",  "y" = "e"^(sqrt"t")`.


If x2 + y2 = 1, then `(d^2x)/(dy^2)` = ______.


State whether the following statement is True or False:

If `sqrt(x) + sqrt(y) = sqrt("a")`, then `("d"y)/("d"x) = 1/(2sqrt(x)) + 1/(2sqrt(y)) = 1/(2sqrt("a"))`


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 ______.


Find `dy/dx` if, `x = e^(3t), y = e^(sqrtt)`


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`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×