Math Insight

Elementary derivative problems

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  1. Calculate the derivative of $\displaystyle v(y) = \frac{- 10 y - 3}{4 \ln{\left (y \right )}}$.
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  2. Differentiate each of the following functions:
    1. $ g(x) = ( 9 x^{2} + 8 x + 7 ) e^x $
    2. $ h(x) = \ln ( x^{3} - 6 x ) $
    3. $f(x) = ( 8 x+ 9 )^4 $

  3. Let $m(y) = a e^{ h y^2 }$, where $a$ and $h$ are parameters (i.e., constant numbers).

    What is $m'(y)$?

    What is $m'(\delta)$?

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  4. Calculate the derivative of $x(t) = (9 t^{3} - 5 t^{2} ) \ln (t)$.
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  5. Compute the derivative of $k(x) = - 10 x^{3} + 10 x^{2} + 8 x - 1$.

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Math 201, Spring 22