If (√(1 − x^2 )) + (√(1 − y^2 )) = a(x − y) then prove that (dy/dx) = (√(((1 − y^2 )/(1 − x^2 )) )) .
If { ((f(x)=x^2 )),((g(x)=sin x)) :}, Then find (df/dg).
How many real solutions does the equation x=sin3x have?
If f(x)=(x!)∙(x!!)∙(x!!!) find (d/dx)(f(x))=?
I=∫_0 ^( ∞) ∫_0 ^( ∞) (( 1)/(1+ x^2 +y^2 +x^2 y^2 )) dxdy=? using polar system...
Donner l′e^ quivalence simple de I_n =∫^( 1) _( 0) (t^n /(t^n −t+1))dt
u_0 = a, u_(n+1) = (√(u_n v_n )) v_0 = b ∈ ]0,1[ , v_(n+1) = (1/(2(u_n +v_n ))) • show that a≤u_n ≤u_(n+1) ≤v_n ≤v_(n+1) ≤b • show that v_n − u_n ≤ ((a+b)/2^n )
x
If x^m .y^n = (x + y)^(m + n) then (d^2 y/dx^2 ) = ?
If e^y (x + 1) = 1 then prove that (d^2 y/dx^2 ) = ((dy/dx))^2 .
If y = (1 + x)(1 + x^2 )(1 + x^4 ) .... (1 + x^(2n) ) then find (dy/dx) at x = 0.
f(x)=tan^2 x (√(tan x((tan x((tan x((tan x(√(...))))^(1/5) ))^(1/4) ))^(1/3) )) f ′((π/4))=?
∫_0 ^( 1) (( ln(1−x )ln(1+x ))/x)dx = Σ_(n=1) ^∞ Ω_n find : Σ_(n=1) ^∞ n Ω_n = ?
ζ
x^3 +y^3 =1 find the implceat second derivative