Answer:
<h3>1/4</h3>
Step-by-step explanation:
Given
amount of salamanders, = 5
amount of crayfish = 3
amount of minnows = 12
Total fish = Total outcome = 5+3+12
Total outcome = 20
Since we are looking for the probability of selecting salamanders, our expected outcome will be 5.
Probability = expected outcome/total outcome
Pr( salamanders,) = 5/20
Pr( salamanders) = 1/4
Hence the probability of selecting salamanders, is 1/4
Answer:
its 4
Step-by-step explanation:
Because since the next number is 8 and its above 5 then a number above 9 is something you cannot put in so you just round the whole number since the rest of the numbers are also 9.
Answer:
![\displaystyle \frac{d}{dx}[e^{2x}] = 2e^{2x}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Be%5E%7B2x%7D%5D%20%3D%202e%5E%7B2x%7D)
![\displaystyle \frac{d}{dx}[e^{3x}] = 3e^{3x}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Be%5E%7B3x%7D%5D%20%3D%203e%5E%7B3x%7D)
General Formulas and Concepts:
<u>Algebra I</u>
- Terms/Coefficients
- Exponential Rule [Multiplying]:

<u>Calculus</u>
Derivatives
Derivative Notation
eˣ Derivative: ![\displaystyle \frac{d}{dx}[e^x] = e^x](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Be%5Ex%5D%20%3D%20e%5Ex)
Derivative Rule [Product Rule]: ![\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5Bf%28x%29g%28x%29%5D%3Df%27%28x%29g%28x%29%20%2B%20g%27%28x%29f%28x%29)
Step-by-step explanation:
<u>Step 1: Define</u>
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<u />
<u />
<u />
<u />
<u>Step 2: Differentiate</u>
<u />
<u />
- [Derivative] Product Rule:
![\displaystyle \frac{d}{dx}[e^{2x}] = \frac{d}{dx}[e^x]e^x + e^x\frac{d}{dx}[e^x]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Be%5E%7B2x%7D%5D%20%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%5Be%5Ex%5De%5Ex%20%2B%20e%5Ex%5Cfrac%7Bd%7D%7Bdx%7D%5Be%5Ex%5D)
- [Derivative] eˣ Derivative:
![\displaystyle \frac{d}{dx}[e^{2x}] = e^x \cdot e^x + e^x \cdot e^x](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Be%5E%7B2x%7D%5D%20%3D%20e%5Ex%20%5Ccdot%20e%5Ex%20%2B%20e%5Ex%20%5Ccdot%20e%5Ex)
- [Derivative] Multiply [Exponential Rule - Multiplying]:
![\displaystyle \frac{d}{dx}[e^{2x}] = e^{2x} + e^{2x}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Be%5E%7B2x%7D%5D%20%3D%20e%5E%7B2x%7D%20%2B%20e%5E%7B2x%7D)
- [Derivative] Combine like terms [Addition]:
![\displaystyle \frac{d}{dx}[e^{2x}] = 2e^{2x}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Be%5E%7B2x%7D%5D%20%3D%202e%5E%7B2x%7D)
![\displaystyle \frac{d}{dx}[e^{3x}]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Be%5E%7B3x%7D%5D)
- [Derivative] Product Rule:
![\displaystyle \frac{d}{dx}[e^{3x}] = \frac{d}{dx}[e^x]e^{2x} + e^x\frac{d}{dx}[e^{2x}]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Be%5E%7B3x%7D%5D%20%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%5Be%5Ex%5De%5E%7B2x%7D%20%2B%20e%5Ex%5Cfrac%7Bd%7D%7Bdx%7D%5Be%5E%7B2x%7D%5D)
- [Derivative] eˣ Derivatives:
![\displaystyle \frac{d}{dx}[e^{3x}] = e^x(e^{2x}) + e^x(2e^{2x})](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Be%5E%7B3x%7D%5D%20%3D%20e%5Ex%28e%5E%7B2x%7D%29%20%2B%20e%5Ex%282e%5E%7B2x%7D%29)
- [Derivative] Multiply [Exponential Rule - Multiplying]:
![\displaystyle \frac{d}{dx}[e^{3x}] = e^{3x} + 2e^{3x}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Be%5E%7B3x%7D%5D%20%3D%20e%5E%7B3x%7D%20%2B%202e%5E%7B3x%7D)
- [Derivative] Combine like terms [Addition]:
![\displaystyle \frac{d}{dx}[e^{3x}] = 3e^{3x}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Be%5E%7B3x%7D%5D%20%3D%203e%5E%7B3x%7D)
Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Derivatives
Book: College Calculus 10e
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