Math Insight

Elementary derivative problems

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  1. Compute the derivative of $g(z) = 7 z^{2} + 8 z + 3$.

  2. Differentiate the function $\displaystyle u(t) = \frac{10 t + 8}{- 8 t + 9}$.

  3. Calculate the derivative of $w(s) = (- 2 s + 3) \ln (s)$.

  4. Differentiate each of the following functions:
    1. $ g(x) = ( 7 x^{2} + 5 x + 8 ) e^x $
    2. $ h(x) = \ln ( x^{3} - 9 x ) $
    3. $f(x) = ( 10 x+ 5 )^4 $

  5. Let $p(x) = k x e^{ c x }$, where $k$ and $c$ are parameters (i.e., constant numbers). What is $p'(x)$? What is $p'(\eta)$?