First Principles Example 2: x³ - Page 6

Questions
  • Can you calculate the first and second derivative of #(x^3+1)/x^2# ?
  • What is the antiderivative of 3^x dx?
  • What is the derivative of #f(x)=(1-cos^2(5x))^3# ?
  • What is the derivative of #(5^xroot4(x^3))/(x^7(x+1)^2)#?
  • If #f(x)=g(x^6)/x^2# , and if g is a differentiable function, find an expression for #f''(x)# ?
  • If #dy/dx# =#3x#+#2/x^2# and y=2 when #x#=1, find the function y?
  • Find #sum_(n=1)^oo n^2/3^n = # ?
  • For the derivative of 6 x^{7} + 3 x^{6} + 6 x^{5}, what is the value of the coefficient of x^{6}?
  • Using the property of derivative differentiate? #root5(x^3)#
  • How do I set this up to verify?
  • Given that x+y=xy show that d^2y/dx^2=2(y/x)^3?
  • What is the differential equation of which #y = (c_1+c_2x)e^x+c_3# is the general solution?
  • How to show that y=3x+(2A/x) is the general solution of the equation x(dy/dx)+y=6x?
  • Find the derivative of the function. #(2x-5)^4(x^2+x+1)^5# ?
  • Find derivative for y=3x^-4 -1/x^2?
  • What is the derivative of #f(x) = lnx^3#?
  • What is dy/dx for 7x^3 + 4y = 3y^2 ?
  • What is the differential wrt x of 3^x lnx ?
  • What is the integral of (1+x)3^x?
  • Fro first principle,find the derivative of Y=5x^3+9?