First Principles Example 1: x² - Page 2

Questions
  • If #dy/dx=2#, why is #dx/dy=1/2#?
  • What is the first derivative of #sin^2(6x)#?
  • If # u = x^2 arctan(x/y) - y^2 arctan(y/x) # then find # (partial ^2u)/(partial x partial y) #?
  • What is the integral of the second derivative?
  • What is the derivative of #x/(x^2+y^2)#?
  • What the derivative of #1/x#?
  • What is #int (1+x)/(1-x) dx# ?
  • Suppose # s(x) # and # c(x) # are 2 functions where: 1) # s'(x) = c(x) # and # c'(x) = -s(x); # 2) # s(0) = 0 # and # c(0) = 1. # What can you say about the quantity: # \qquad [ s(x) ]^2 + [ c(x) ]^2 # ?
  • What is the derivative of #x^2+y^2#?
  • Y'= (x^2 - xy +y^2)/xy how to do ?
  • What is the differentiate of -2x/(1+x^2)^2?
  • How can I solve this differential equation? x dy/dx+y=x^2y^2
  • How to find #dy/dx# from #x^2y+3xy^2-x=5#?
  • Consider the function f(x)=x²-3x-4 Evaluate f ′(-2) using the definition of the derivative?
  • What is the Derivative of 4x?
  • Can someone solve this...xyy'=1-x^2?....thanks :)
  • Find the initial value problem in #dy/dx=(y^2+4x^2)/(4xy)#?
  • What is the 20th derivative of x∧-2?
  • How to check work for First Order Linear Differential Equation?
  • Xy^2dy=-(y+1)dx how to do ?