Math 181 Miniproject 3: Texting Lesson.md
---
My lesson Topic
===

<style>
body {
background-color: #eeeeee;
}

h1 {
color: maroon;
margin-left: 40px;
}

.gray {
margin-left: 50px ;
margin-right: 29%;
font-weight: 500;
color: #000000;
background-color: #cccccc;
border-color: #aaaaaa;
}

.blue {
display: inline-block;
margin-left: 29% ;
margin-right: 0%;
width: -webkit-calc(70% - 50px);
width: -moz-calc(70% - 50px);
width: calc(70% - 50px);
font-weight: 500;
color: #fff;
border-color: #336699;
background-color: #337799;
}

.left {
content:url("https://i.imgur.com/rUsxo7j.png");
width:50px;
border-radius: 50%;
float:left;
}
.right{
content:url("https://i.imgur.com/5ALcyl3.png"); width:50px;
border-radius: 50%;
display: inline-block;
vertical-align:top;
}
</style>

<div id="container" style=" padding: 6px;
color: #fff;
border-color: #336699;
background-color: #337799;
display: flex;
justify-content: space-between;
margin-bottom:3px;">
<div>
<i class="fa fa-envelope fa-2x"></i>
</div>
<div>
<i class="fa fa-camera fa-2x"></i>
</div>

<div>
<i class="fa fa-comments fa-2x"></i>
</div>
<div>
<i class="fa fa-address-card fa-2x" aria-hidden="true"></i>
</div>
<div>
<i class="fa fa-phone fa-2x" aria-hidden="true"></i>
</div>
<div>
<i class="fa fa-list-ul fa-2x" aria-hidden="true"></i>
</div>
<div>
<i class="fa fa-user-plus fa-2x" aria-hidden="true"></i>
</div>
</div>

<div><img class="left"/><div class="alert gray">

Hey, I'm having some issues with the lesson. do you think you could help me out with a problem?

</div></div>

<div><div class="alert blue">

Sure, what's the problem about?

</div><img class="right"/></div>

<div><img class="left"/><div class="alert gray">

It's about the basic derivative rules, but like especially when it comes to sum of power functions. Like I'm not sure where to start. Here look at the equation I'm supposed to differentiate.

</div></div>

<div><img class="left"/><div class="alert gray">

$$y=5x^{6}-2\sqrt{x}+\frac{5}{x}+5$$

</div></div>

<div><div class="alert blue">

Ok, that's not too bad. We just have to break it down into its components. First, you have to understand that certain patterns arise from applying the Limit Definition of the derivative to certain functions. It is from these patterns that we can begin to establish rules for simplifying finding the derivative of a function.

</div><img class="right"/></div>

<div><img class="left"/><div class="alert gray">

Ok, so I know what a derivative is, as far as the slope of a function.

</div></div>

<div><div class="alert blue">

Right, so we can begin by applying rules to the components of that equation to reach the derivative. You should look into the constant function rule and power function rule. Have you seen them yet? Try to apply them individually first.

</div><img class="right"/></div>

<div><img class="left"/><div class="alert gray">

Ok, so beginning with the constant function rule $f(x) = c$ then $f'(x) = 0$, and I can apply that to the only constant in the equation, the single +5 term which will have a derivative of 0. For the $5x^6$ term I use the Power Rule $f(x)=x^n$ $f'(x)=nx^n−1$ and derive $30x^5$. But if I rewrite $-2\sqrt{x}$ as $-2x^{1/2}$ I can derive ${-1}x^{-1/2}$. I can do the same thing to the $5/x$ term, rewriting it as $5x^{-1}$, and derive $-5x^{-2}$. The sum rule of derivatives states that if f(x) and g(x) are differentiable functions, then the derivative of f(x)+g(x) will be simply f'(x)+g'(x). This means that I can just add the derivatives I've already worked out. So my final solution should be $30x^5−{1/x}−{5/x^2}$.

</div></div>

<div><div class="alert blue">

Perfect! You got it!

</div><img class="right"/></div>

---

To submit this assignment click on the Publish button . Then copy the url of the final document and submit it in Canvas.