Exercises - Simple Differentiation Rules

  1. Find the derivative of each function given

    1. $\displaystyle{f\,(x) = 4}$

    2. $\displaystyle{f\,(x) = e^{\pi}}$

    3. $\displaystyle{f\,(x) = \sqrt{2}}$

  2. Find $f\,'(x)$ for each function below

    1. $\displaystyle{f\,(x)=x^4}$

    2. $\displaystyle{f\,(x)=x^{100}}$

    3. $\displaystyle{f\,(x)=4x^3}$

    4. $\displaystyle{f\,(x)=\frac{1}{2} x^{2/3}}$

    5. $\displaystyle{f\,(x)=4x^{-1/4}}$

    6. $\displaystyle{f\,(x)=\pi x^{\sqrt{2}}}$

  3. In each case, find $y'$

    1. $\displaystyle{y = 4\sqrt{x}+\frac{3}{x}-5x+4}$

    2. $\displaystyle{y = \frac{2}{\sqrt{x}} + \frac{\sqrt{x}}{2} + \frac{1}{x} - x}$

    3. $\displaystyle{y = \sqrt{x} + \frac{1}{\sqrt{x}} + \frac{3}{x} - 3x}$

  4. Differentiate, simplifying your result as appropriate

    1. $\displaystyle{f\,(x) = 7x^3+6x^2+10x+12}$

    2. $\displaystyle{f\,(x) = 3x^3-6x^{-2}+x^{-7}-x^{-6}}$

  5. Find the equation of the tangent line to $y=x^3+3x^2+3x+9$ where $x=-3$