English

If `Xpowerm Ypowern = (X + Y)Power(M + N)`, Prove that `(Dsquare2y)/(Dxsquare2)= 0`

Advertisements
Advertisements

Question

if `x^m y^n = (x + y)^(m + n)`, prove that `(d^2y)/(dx^2)= 0`

Advertisements

Solution

We are given

`x^m y^n = (x + y)^(m + n)`

Taking log on both sides, we get

shaalaa.com
  Is there an error in this question or solution?
2016-2017 (March) Delhi Set 1

RELATED QUESTIONS

 

If `y=log[x+sqrt(x^2+a^2)]` show that `(x^2+a^2)(d^2y)/(dx^2)+xdy/dx=0`

 

 

if xx+xy+yx=ab, then find `dy/dx`.


Differentiate the function with respect to x.

(log x)cos x


Differentiate the function with respect to x.

xx − 2sin x


Find `bb(dy/dx)` for the given function:

(cos x)y = (cos y)x


Find the derivative of the function given by f(x) = (1 + x) (1 + x2) (1 + x4) (1 + x8) and hence find f′(1).


If x = a (cos t + t sin t) and y = a (sin t – t cos t), find `(d^2y)/dx^2`.


Find `dy/dx` if y = x+ 5x


Differentiate : log (1 + x2)  w.r.t. cot-1 x. 


If log (x + y) = log(xy) + p, where p is a constant, then prove that `"dy"/"dx" = (-y^2)/(x^2)`.


If xy = ex–y, then show that `"dy"/"dx" = logx/(1 + logx)^2`.


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


If x = a cos3t, y = a sin3t, show that `"dy"/"dx" = -(y/x)^(1/3)`.


Differentiate 3x w.r.t. logx3.


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


Choose the correct option from the given alternatives :

If xy = yx, then `"dy"/"dx"` = ..........


If y = `25^(log_5sin_x) + 16^(log_4cos_x)` then `("d"y)/("d"x)` = ______.


If y = `log[sqrt((1 - cos((3x)/2))/(1 +cos((3x)/2)))]`, find `("d"y)/("d"x)`


If log5 `((x^4 + "y"^4)/(x^4 - "y"^4))` = 2, show that `("dy")/("d"x) = (12x^3)/(13"y"^2)`


If x7 . y5 = (x + y)12, show that `("d"y)/("d"x) = y/x`


`log (x + sqrt(x^2 + "a"))`


`log [log(logx^5)]`


If y = `(1 + 1/x)^x` then `(2sqrt(y_2(2) + 1/8))/((log  3/2 - 1/3))` is equal to ______.


If y = `x^(x^2)`, then `dy/dx` is equal to ______.


Derivative of log (sec θ + tan θ) with respect to sec θ at θ = `π/4` is ______.


If `log_10 ((x^2 - y^2)/(x^2 + y^2))` = 2, then `dy/dx` is equal to ______.


If y = `log(x + sqrt(x^2 + 4))`, show that `dy/dx = 1/sqrt(x^2 + 4)`


If xy = yx, then find `dy/dx`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×