Proof of the Product Rule - Page 2

Questions
  • What is #lim_(x->oo) (ln(x+1) - ln(x-1))/(1/x)#?
  • How do we derive the product rule?
  • Find two positive numbers whose sum is 18 and the product of the first number and the square of the other is a maximum. Help!?
  • Can anyone help me, please? #intdx/(x^2-4x-13#
  • What is the jacobian of #bb(F)((x),(y)) = ( (ycosx) ,(x-y+2)) #?
  • How to prove or dis prove ? #if lim_(x->a)f(x)=b and lim_(x->b)g(x)=c# then #lim_(x->a)g๐f(x)=c#
  • How do you differentiate the equation?
  • Show that if # u = arcsin( (x^2+y^2)/(x+y) ) # then #u# is a solution of the PDE #x(partial u)/(partial x) + y(partial u)/(partial y) ={ (x^2+y^2)/(x+y) }/( sqrt(1-((x^2+y^2)/(x+y))^2) )#?
  • How do you demonstrate that, if #(df)/(dr)= (dg)/(dy)#, then #(df)/(dr)= (dg)/(dy) = K # where K is a constant ?
  • Show that limit of (4^x-4)/(x-1)=8log2 as x approaches to 1?
  • Find the derivative using the derivative rules?
  • Could you differentiate this function? f(x)=6x^2ln(4x)
  • Differentiate the following functions (a), (b), (c).?
  • How can I solve this problem?Please,help.
  • How to solve the mentioned problem?
  • Prove by induction: d^2n/dx^2n (xsinsx)=(-1)^n (xsins-2ncosx)?
  • Starting with #(epsilonA_(s,r)sigma)/(rhoVc)int_(0)^(t)dt = int_(T_i)^(T) 1/(T_(sur)^4 - T^4)dT#, show that . . . ?
  • Prove using the formal definition of a derivative that (f-g)'(x)= f'(x)-g'(x)?
  • (The function is cubed) How do you find a and b?
  • How do you find the constants a and b?