First Principles Example 3: square root of x - Page 4

Questions
  • What is the derivative of the following function? f(x)=ln(sqrt(x^sin(x)))
  • If #f(x)=5e^x+9ln(x)#, what is #f'(3)#?
  • What is the derivative of #f(x) = lnsqrtx#?
  • What is the derivative of #f(x) = ln(x^2+1)#?
  • What is the derivatie of ln (x) / (1 - ln(x))?
  • What is the derivative of #f(x) = (1+lnx)^2/(1-lnx)#?
  • Find the number most exceeded by its square root?
  • Differentiate #(sqrt(x) + 1 )^2/ x# with respect to #X.#?
  • How do I derive #y=sqrt(9+x^2)+sqrt(x^2-10x+41)#?
  • Solve: Lim #x->1# #(sqrt(x)-sqrt(2-x^2))/(2x-sqrt(2+2x^2)# ?
  • What is the derivative of #(x-1)/sqrtx#?
  • What is the derivative of #f(x) = sqrt((lnx)^2+x^3-5)#?
  • Determine a function #h# such that #d/(dx)[sqrt(h(x))] = (3x^2)/(2sqrt(x^3+4))?#
  • How do you find the derivative of #f(x) = sqrt(ax+b)# by first principles?
  • My friend gave me a nasty integral: #int sqrt{1 + (-sin(0.7x^{1.18})0.826x^{0.18})} dx#. Can anybody give me some advice on how to solve this?
  • Determine a function #h# such that #d/(dx) [sqrt(h(x))]=(3x^2)/(2sqrt(x^3+4))#?
  • How do you solve #y=int_sqrtx^(x^3) sqrtt sintt # #d##t#?
  • Can we write it like this?
  • How do you evaluate #int sqrt(9-x^2) dx#?
  • What is the integral of #(1/sqrt(4-x^2))#?