Calc I: In class practice for quiz 2

Here are a few more practice problems for our next quiz this Friday.

Problems

  1. Let \(f(x) = 101^x\).

    1. Write down the difference quotient for \(f\).
    2. Use a little algebra to separate out the \(x\)s and \(h\)s in your difference quotient.

  2. Use the differentiation rules to compute the derivatives of the following functions:

    1. \(\displaystyle f(x) = 101^x\)
    2. \(\displaystyle f(x)=e^{2x+3}\)
    3. \(\displaystyle f(x)=\ln(4x^2+1)\)
    4. \(\displaystyle f(x)=x^3e^{-x}\)
    5. \(\displaystyle f(x)=(2x^2-5x+1)2^x\)
    6. \(\displaystyle f(x)=\frac{e^x}{x^2+1}\)