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Derivative-practice-basics.tex
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Derivative-practice-basics.tex
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\Section{Derivative practice---basics}
\begin{ProblemSet}
\begin{Problem}
What is $f'(x)$?
\begin{equation*}
f(x) = 3 x + 7
\end{equation*}
\end{Problem}
\begin{Problem}
What is $g'(x)$?
\begin{equation*}
g(x) = x^3 + x^4
\end{equation*}
\end{Problem}
\begin{Problem}
What is $h'(x)$?
\begin{equation*}
h(x) = 10 x^3 - x^4
\end{equation*}
\end{Problem}
\begin{Problem}
What is $u'(t)$?
\begin{equation*}
u(t) = 5 \left(t^3 + t^4\right)
\end{equation*}
\end{Problem}
\begin{Problem}
What is $v'(t)$?
\begin{equation*}
v(t) = \left(t^5 - 8 t\right) \times 4
\end{equation*}
\end{Problem}
\begin{Problem}
What is $w'(t)$?
\begin{equation*}
w(t) = t^{-4}
\end{equation*}
\end{Problem}
\begin{Problem}
What is $p'(z)$?
\begin{equation*}
p(z) = \sqrt{z}
\end{equation*}
\end{Problem}
\begin{Problem}
What is $q'(z)$?
\begin{equation*}
q(z) = \frac{1}{z}
\end{equation*}
\end{Problem}
\begin{Problem}
What is $r'(z)$?
\begin{equation*}
r(z) = \frac{1}{\sqrt{z}}
\end{equation*}
\end{Problem}
\begin{Problem}
What is $f'(x)$?
\begin{equation*}
f(x) = \frac{4}{x} + 6 \sqrt{x}
\end{equation*}
\end{Problem}
\begin{Problem}
What is $g'(x)$?
\begin{equation*}
g(x) = x (x + 1)
\end{equation*}
\end{Problem}
\begin{Problem}
What is $h'(w)$?
\begin{equation*}
h(w) = \frac{5 w^2 - 6 w^3}{w}
\end{equation*}
\end{Problem}
\begin{Problem}
What is $q'(x)$?
\begin{equation*}
q(x) = 16 \sqrt{x}
\end{equation*}
\end{Problem}
\begin{Problem}
What is $r'(x)$?
\begin{equation*}
r(x) = \sqrt{16 x}
\end{equation*}
\end{Problem}
\begin{Problem}
What is $m'(s)$?
\begin{equation*}
m(s) = 7 \sqrt{s}
\end{equation*}
\end{Problem}
\begin{Problem}
What is $n'(s)$?
\begin{equation*}
n(s) = \sqrt{7 s}
\end{equation*}
\end{Problem}
\begin{Problem}
What is $\Deriv{y}{x}$?
\begin{equation*}
y = 6 x^2 - 4 x + 10
\end{equation*}
\end{Problem}
\begin{Problem}
What is $\Deriv{p}{r}$?
\begin{equation*}
p = 10 - \frac{5}{r^2}
\end{equation*}
\end{Problem}
\begin{Problem}
What is $\Deriv{y}{x}$?
\begin{equation*}
y = x
\end{equation*}
\end{Problem}
\begin{Problem}
What is $\Deriv{u}{t}$?
\begin{equation*}
u = 42
\end{equation*}
\end{Problem}
\begin{Problem}
What is $\Deriv{w}{z}$?
\begin{equation*}
w = \sqrt{5}
\end{equation*}
\end{Problem}
\begin{Problem}
What is $\Deriv{b}{q}$?
\begin{equation*}
b = q^2 + 6^2 q + 5^2
\end{equation*}
\end{Problem}
\begin{Problem}
What is $u'(t)$?
\begin{equation*}
u(t) = \frac{t^2 + 5 t + 3}{2}
\end{equation*}
\end{Problem}
\begin{Problem}
What is $v'(t)$?
\begin{equation*}
v(t) = \frac{t^2 + 5 t + 3}{t}
\end{equation*}
\end{Problem}
\end{ProblemSet}
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