<span>−12x3y5 − 9x2y2 + 12xy3</span>
-3xy^2(4x^2y^3+3x-4y)
Answer:

General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Geometry</u>
Area of a Rectangle: A = lw
<u>Calculus</u>
Derivatives
Derivative Notation
Implicit Differentiation
Differentiation with respect to time
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>
<u />
<u />
<u />
<u />
<u />
<u />
<u />
<u />
<u />
<u>Step 2: Differentiate</u>
- [Area of Rectangle] Product Rule:

<u>Step 3: Solve</u>
- [Rate] Substitute in variables [Derivative]:

- [Rate] Multiply:

- [Rate] Add:

Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Implicit Differentiation
Book: College Calculus 10e
Answer:

Step-by-step explanation:
Given
![\sqrt[3]{217}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B217%7D)
Required
Solve
Linear approximated as:

Take:

So:
![f(x) = \sqrt[3]{x}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Csqrt%5B3%5D%7Bx%7D)
Substitute 216 for x
![f(x) = \sqrt[3]{216}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Csqrt%5B3%5D%7B216%7D)

So, we have:



To calculate f'(x);
We have:
![f(x) = \sqrt[3]{x}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Csqrt%5B3%5D%7Bx%7D)
Rewrite as:

Differentiate

Split


Substitute 216 for x



So:





C - no solution
you take the second solution and times the entire equation by -1
then simply
and you get 0x + 0y = 20
THE EQUATION TO THIS PROBLEM IS y=2x+12