Question

Differentiate the following with respect to x
${ {e}^{x} }^{3}$
${ {e}^{sin^{x} }$
please help ​

Answer 1

Answer:

math formulas set "inline", and a display math mode, used for displayed math form

\[

\left|\sum_{i=1}^n a_ib_i\right|

\le

\left(\sum_{i=1}^n a_i^2\right)^{1/2}

\left(\sum_{i=1}^n b_i^2\right)^{1/2}

\]

Exercise 2.4: Typeset the above expression and look at the output. (It's a famous mathematical theorem!). Then remove, or comment out, one of the bracket expressions (say, one instance of "\left("), and see what error messages you get. All bracket expressions generated by \left.. or \right.. must occur in pairs, and TeX gives an error message if this is not the case. (The left and right brackets don't have to be of the same type; for example, $\left\[\frac{3}{4}, \frac{4}{5}\right[$ to denote the half-open interval [3/4, 4/5[ is perfectly legal.)

Displayed equations

Single line displays: To get a single line, displayed equation (without equation number), just use the pair "\[", "\]". If you want TeX to automatically number the equation, use instead the \begin{equation} ... \end{equation} environment. (The asterisk variant, \begin{equation*} ... \end{equation*}, turns off the equation numbering, and is equivalent to typing \[ ... \].)

Multi-line equation environments: Things get more complicated if you have multiline equations that need to be lined up at suitable places. For most situations, the \begin{align} ... \end{align} environment, and its variant \begin{align*} ... \end{align*}, are sufficient. As with the equation environment, the asterisk version does not automatically number equations.

The use of align is best illustrated with an example:

\begin{align}

(a+b)^3 &= (a+b)^2(a+b)\\

&=(a^2+2ab+b^2)(a+b)\\

&=(a^3+2a^2b+ab^2) + (a^2b+2ab^2+b^3)\\

&=a^3+3a^2b+3ab^2+b^3

\end{align}

.

Exercise 2.6

Step-by-step explanation:

pllz give me one brilient