Math Insight

Elementary derivative problems

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  1. Calculate the derivative of $v(t) = (- 8 t^{3} + t^{2} ) \ln (t)$.
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  2. Differentiate each of the following functions:
    1. $ g(x) = ( 6 x^{2} + 5 x + 2 ) e^x $
    2. $ h(x) = \ln ( x^{3} - 6 x ) $
    3. $f(x) = ( 8 x+ 6 )^4 $

  3. Compute the derivative of $h(t) = - 9 t^{3} - 10 t^{2} + t + 3$.

  4. Let $p(z) = b e^{ c z^2 }$, where $b$ and $c$ are parameters (i.e., constant numbers).

    What is $p'(z)$?

    What is $p'(\xi)$?

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  5. Let $\displaystyle f(z) = \frac{5 z - 2}{9 \ln{\left (z \right )}}$. Find $\displaystyle \frac{d f}{d z}$.
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Math 201, Spring 22