मराठी

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

Advertisements
Advertisements

प्रश्न

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

Advertisements

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
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
2016-2017 (March) All India Set 1

संबंधित प्रश्‍न

Find `bb(dy/dx)` in the following:

ax + by2 = cos y


Show that the derivative of the function f given by 

\[f\left( x \right) = 2 x^3 - 9 x^2 + 12x + 9\], at x = 1 and x = 2 are equal.

Discuss extreme values of the function f(x) = x.logx


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


Find `"dy"/"dx"`, if : `x = cos^-1(4t^3 - 3t), y = tan^-1(sqrt(1 - t^2)/t)`.


Find `"dy"/"dx"` if : x = cosec2θ, y = cot3θ at θ= `pi/(6)`


Differentiate `sin^-1((2x)/(1 + x^2))w.r.t. cos^-1((1 - x^2)/(1 + x^2))`


Differentiate `tan^-1((x)/(sqrt(1 - x^2))) w.r.t. sec^-1((1)/(2x^2 - 1))`.


Differentiate `tan^-1((sqrt(1 + x^2) - 1)/(x)) w.r.t  tan^-1((2xsqrt(1 - x^2))/(1 - 2x^2))`.


Find `(d^2y)/(dx^2)` of the following : x = sinθ, y = sin3θ at θ = `pi/(2)`


Find `(d^2y)/(dx^2)` of the following : x = a cos θ, y = b sin θ at θ = `π/4`.


If `sec^-1((7x^3 - 5y^3)/(7^3 + 5y^3)) = "m", "show"  (d^2y)/(dx^2)` = 0.


If x = a sin t – b cos t, y = a cos t + b sin t, show that `(d^2y)/(dx^2) = -(x^2 + y^2)/(y^3)`.


Find the nth derivative of the following : (ax + b)m 


Find the nth derivative of the following : cos (3 – 2x)


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(x)(3 - x))/(1 - 3x))`


If sin y = x sin (a + y), then show that `"dy"/"dx" = (sin^2(a + y))/(sina)`.


Differentiate `tan^-1((sqrt(1 + x^2) - 1)/x)` w.r.t. `cos^-1(sqrt((1 + sqrt(1 + x^2))/(2sqrt(1 + x^2))))`


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


Choose the correct alternative.

If x = `("e"^"t" + "e"^-"t")/2, "y" = ("e"^"t" - "e"^-"t")/2`  then `"dy"/"dx"` = ? 


If y = `sqrt(tansqrt(x)`, find `("d"y)/("d"x)`.


If `sqrt(x) + sqrt(y) = sqrt("a")`, then `("d"y)/("d"x)` is ______


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


Find `(d^2y)/(dy^2)`, if y = e4x


Solve the following.

If log(x + y) = log(xy) + a then show that, `dy/dx = (-y^2)/x^2`


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


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


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×