Proof of Quotient Rule - Page 2

Questions
  • How do you find the limit of #\lim _ { x \rightarrow 3} 5\cdot \frac { \sqrt { x + 1} - 2} { x - 3}#?
  • Differentiate #y=(x+1)^(1/2)+(x+1)^(-1/2)# using quotient formula?
  • How do you differentiate #f(x)=(x^3-3x^2-3x-6)/((x-6)(x-1)# using the quotient rule?
  • Differentiate #y=f(x)=1/sqrt(1-x)# using the definition of derivative #(dy)/(dx)=lim_(h->0)(f(x+h)-f(x))/h#?
  • How do you find the difference quotient of #f#, that is, find #((f(x+h)-f(x))/h)#, #h != 0# for #f(x)=x^2-5x+7#?
  • If z = f(x,y) and x^2 + 2xz - 2yz^2 = 10....?
  • Let #f(x) = 5 + 3 x^2#. If h cannot equal 0, then the difference quotient can be simplified as (f(x+h)-f(x))/h = Ah + Bx + C,?
  • Show that #lim_(x to +oo)f'(x)=0# ?
  • Be f : A → B a function and X,Y ⊂ A. Show that: any thoughts? thanks
  • How do you show that if #y=sqrt(x+sqrt(x^2+1)#, then #y'=(sqrt(x+sqrt(x^2+1))/(2sqrt(x^2+1)))# ?
  • Evaluate the limit as x approaches 1 of the quotient of the square root of the quantity x squared plus 3 minus 2 and the quantity x minus 1. You must show your work to receive credit?
  • How do i find the answer using the quotient rule for this question?
  • Differentiate and simplify!!! Please help?
  • What does (x^3-a^3)/(x^4-a^4) equal when the limiting factor is x approaches a? Thank you!!!
  • Which of the following statements are true or false?Please give reasons for your answers. (i)The derivative of quotient of two functions is equal to the quotient of derivatives of two functions.
  • How do you differentiate f(x)=(x-x^1/2)/x^1/9?
  • Help me to proof this L'Hospital's Rule II for case (b) please? I am waiting for your help. Thank you very much for your help before.
  • How do you prove #d/dx##(1-x^2) = -2x# using the limit definition of the derivative?
  • How to differentiate #y= (ln(4x^2))/(3^(6x)# ?
  • How could I prove this? Would this be using a theorem from real analysis?