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Practice Problems for 3/11

  1. Let \(f(x)=5x^2-10x+4\), for \(x\geq 1\). Find the value of the derivative of \(f^{-1}(x)\) at \(x=4=f(2)\).

  2. Find the derivative of the following with respect to the independent variable.

    1. \(f(x)=\left(\frac{3}{4}\right)^{2x}\)
    2. \(g(s)=\log_5(s^2+s),\quad s>0\)
    3. \(s(t)=\log_3(3^{t^4})\)
  3. Use the product rule to find the derivative of \(y=x^2(7x^3+4)^6(x^2+1)\). (Or at least carry our the first two or three steps to get an idea of how using the product rule within the product rule would go.)