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Elementary derivative problems

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

  2. Calculate the derivative of $\displaystyle m(y) = \frac{2 e^{y}}{- 5 y + 5}$.
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  3. Calculate the derivative of $v(t) = (- t - 5) \ln (t)$.
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  4. Let $v(z) = b z e^{ a z }$, where $b$ and $a$ are parameters (i.e., constant numbers). What is $v'(z)$? What is $v'(\xi)$?

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  5. Compute the derivative of $h(x) = 5 x^{3} + 9 x - 9$.

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Math 1241, Fall 2020