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Elementary derivative problems

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  1. Let $\displaystyle u(t) = \frac{- 2 t + 3}{- t - 10}$. Find $\displaystyle \diff{ u }{ t }$.
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  2. Error in question

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    • Error in expression: differentpars
      Could not determine truth value of required condition Not(Eq(par1,par2)), evaluated as: b != a
    Let $m(z) = b e^{ a z^2 }$, where $b$ and $a$ are parameters (i.e., constant numbers). What is $\displaystyle \diff{ m }{ z }$? What is $\displaystyle\diff{ m }{ z }\bigg|_{ z= \nu }$?
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  3. Let $h(x) = - 7 x^{3} - 3 x^{2} - 8 x - 2$. Find a linear function that is a good approximation of $h$ for values of $x$ near $7$.
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  4. Calculate the derivative of $u(s) = (6 s^{3} - 7 s^{2} ) \ln (s)$.
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  5. Differentiate each of the following functions:
    1. $ g(x) = ( 7 x^{2} + 2 x + 9 ) e^x $
    2. $ h(x) = \ln ( x^{3} - 9 x ) $
    3. $f(x) = ( 4 x+ 6 )^4 $

  6. Let $y(t) = (10 t^{3} + 8 t^{2}) \ln (t)$. What is the slope of the tangent line to the graph of $y$ at the point $t=2$. At the point $t=\Diamond$?
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  7. Compute the derivative of $k(z) = 4 z^{2} - 8 z + 1$.

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Math 201, Spring 2015