First Principles Example 2: x³ - Page 5

Questions
  • What is the #n^"th"# derivative of #x/(x-1)#?
  • Show that if # u = arctan( (x^3+y^3)/(x-y) ) # then #u# is a solution of the PDE #x(partial u)/(partial x) + y(partial u)/(partial y)=2( (x-y)(x^3+y^3) ) /( (x-y)^2+(x^3+y^3)^2 )#?
  • How do you find the derivative of #y=ln(tg^3(x/6))#?
  • State the Derivative of #x# State the Derivative of #1/x# ?
  • What is the gradient of the tangent to the curve of #y=x^3-3x# at the point where #x=5#?
  • What the second derivative? #x^(2/3)+ y^(2/3) = 1# Help me please
  • How do you use implicit differentiation to find #y'# and evaluate #y'# at #(1,1)# for #xln(y) + 6y = 2x^3#?
  • If #(x+1)^n = sum_(k=0)^n c_k x^k# then show #sum_(k=0)^n 3^k c_k = 2^(2n)# ?
  • How do I find the #lim_(x to 6) (5x)/(3+x^8)#?
  • Could you please show me how to do this?
  • What is the partial derivative of #e^(xy) = ye^(xy)# wrt #x#?
  • #xy^2*(dy/dx)=y^3-x^3, y(1)=2# (its a initial value problem) Any kind soul here who can give the solution of this eqn?
  • Let f(x)=-2x^3+5x^2-3x-3 find an expression for the second derivative f''(x)?
  • Given that # p(x) = ((x+x^4+x^7)^10)((1+x^2)^11)(x^3+x^4+x^8) #, what is the 100th derivative?
  • Can someone tell me where my error is in finding the derivative of #y=x^(lnx)#?
  • Find the differential of #y=log((1+x^2)/(1-x^2))#?
  • What is the derivative of #f(x) = 3^(2x)/x#?
  • What is the derivative of (ln x)^3?
  • What is the first differential of #y=2ln(2/(3x))# ?
  • How to separate variable equation #dy/dx = (xy+x)^(2/3) #?