Basic Calculus: Practice Exercises

  • Determine the following derivatives and evaluate the following integrals, all by hand. You should also learn how to check these answers on Wolfram Alpha.
    1. \(\frac{d}{du}\left(u^2\sin u\right)\)
    2. \(\frac{d}{dz}\left(\ln(z^2+1)\right)\)
    3. \(\displaystyle\int v\cos(v^2)\,dv\)
    4. \(\displaystyle\int v\cos v\,dv\)