Calculate the derivative of the following function f(x)-\ln\frac{(2x-1)(x+2)^3}{(1-4x)^2}

Let B be a 4x4 matrix to which we apply the following operations:
1. double column 1,
2. halve row 3,
3. add row 3 to row 1,
4. interchange columns 1 and 4,
5. subtract row 2 from each of the other rows,
6. replace column 4 by column 3,
7. delete column 1 (column dimension is reduced by 1).
(a) Write the result as a product of eight matrices.
(b) Write it again as a product of ABC (same B) of three matrices.

Find a basis for the space of $2\times 2$ diagonal matrices.
$\text{Basis }=\{\left[\begin{array}{cc}& \\ & \end{array}\right],\left[\begin{array}{cc}& \\ & \end{array}\right]\}$

What is ${\displaystyle 7+6i}$ divided by ${\displaystyle 10+i}$?

Consider the three following matrices:
$A=\left[\begin{array}{ccc}1& 0& 0\\ 0& -1& 0\\ 0& 0& 1\end{array}\right],B=\left[\begin{array}{ccc}1& 0& 0\\ 0& 0& 0\\ 0& 0& -1\end{array}\right]\text{ and }C=\left[\begin{array}{ccc}0& -i& 0\\ i& 0& -i\\ 0& i& 0\end{array}\right]$
Calculate the Tr(ABC)
(a)1
(b)2
(c)2i
(d)0

For the following exercises, enter the data from each table into a graphing calculator and graph the resulting scatter plots. Determine whether the data from the table could represent a function that is linear, exponential, or logarithmic. $\begin{array}{|ccccccccccc|}\hline x& 1& 2& 3& 4& 5& 6& 7& 8& 9& 10\\ f(x)& 2.4& 2.88& 3.456& 4.147& 4.977& 5.972& 7.166& 8.6& 10.32& 12.383\\ \hline\end{array}$

How do you multiply ${\displaystyle (-2-8i)(6+7i)}$?

Trigonometric equation: ${\displaystyle {\ln (\sin x+\cos x)}^{1+\sin 2x}=2}$