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Errors occurred in the following questions: 3

Elementary derivative problems

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  1. Compute the derivative of $h(t) = 8 t^{3} - t^{2} + 5 t - 7$.

  2. Calculate the derivative of $v(s) = (5 s - 4) \ln (s)$.
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  3. Error in question

    The following errors occurred when rendering the question:

    • Error in expression: differentpars
      Could not determine truth value of required condition Not(Eq(par1,par2)), evaluated as: k != h
    Let $w(t) = k e^{ h t^2 }$, where $k$ and $h$ are parameters (i.e., constant numbers). What is $\displaystyle \diff{ w }{ t }$? What is $\displaystyle\diff{ w }{ t }\bigg|_{ t= \eta }$?
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  4. Let $\displaystyle f(s) = \frac{7 s - 2}{3 s - 4}$. Find $\displaystyle \diff{ f }{ s }$.
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  5. Differentiate each of the following functions:
    1. $ g(x) = ( 10 x^{2} + 7 x ) \ln (x) $
    2. $ h(x) = e^{ x^{3} - 3 x } $
    3. $f(x) = ( 5 x+ 6 )^4 $

  6. Let $k(q)=e^{ -2 q^2 +3q -7 }$. Find the equation for the tangent line of the graph of $k$ at $q=1$.
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  7. Let $y(t) = (- 6 t^{3} + 4 t^{2}) \ln (t)$. What is the slope of the tangent line to the graph of $y$ at the point $t=5$. At the point $t=\bigcirc$?
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Math 201, Spring 2015