From First Principles

"From First Principles" is a foundational concept that underpins various disciplines, from philosophy to physics, and entrepreneurship to engineering. It involves breaking down complex problems into their fundamental components and building understanding from the ground up. By starting with basic truths and axioms, individuals can derive new insights and solutions, free from conventional thinking or assumptions. This approach fosters creativity, innovation, and a deeper understanding of the subject matter. Whether in scientific research, business strategy, or personal development, embracing the principle of "From First Principles" empowers individuals to question, explore, and create in a manner that is both rigorous and transformative.

  • Prove using the first principals that #d/dx(lnx) =1/x# ?
  • Find the derivative of #cscx# from first principles?
  • How do you differentiate f(x)=#1/sqrt(x-4)# using first principles?
  • Differentiate #xsinx# using first principles?
  • Prove that #lim_(x rarr2) ( 2^x-4 ) / (x-2) =ln16#?
  • Differentiate #e^(ax)# using first principles?
  • What is the derivative of #e^(9x)#?
  • How can I find the derivative of #y=e^x# from first principles?
  • How will you answer this?
  • Let F(x) be the cdf of the continuous-type random variable X, and assume that F(x)=0 for x<=0 and 0<F(x),1 for 0<x. Prove that if P(X>x+y|X>x)=P(X>y), then F(x)=1-#e^(-lamdax# , 0<x ?
  • If # G(x)=f(ax+b) # then prove that # G^((n))(x)=a^nf^((n))(ax+b) #?
  • What is the correct way to solve this? Explain step by step.
  • Find the differential of #f(x)=x^20# using first principal?
  • Suppose a snowboard manufacturer will sell q snowboards per week when charging p dollars per snowboard where q= (600−p)^3. Find the price the company should charge to maximize revenue? (Recall:R=pq, revenue equals quantity times price.)
  • How do I even approach this problem? I don't know where to start.
  • How do I find the answer?
  • Help with this? Suppose a function f is 26 times differentiable and f^(26)=f. Then, it turns out that f is infinitely differentiable and that for any positive number n, f^(n) equals one of the functions f,f′,f′′,...,f^(25).
  • What is the ifferential equation of the family of hyperbolas: #x^2/a^2 + y^2/b^2 = 1#?
  • Differentiate y=x^n using first principle?
  • Please can anyone help me integrate sec^nx with step-by-step formular?