Question

PLEASE HELP!!!
d/dx(e^2x)=d/dx(e^x*e^x)=?

Answer 1

`\displaystyle (d)/(dx)[e^(2x)] = 2e^(2x)`

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

Calculus

Derivatives

Derivative Notation

Derivative Rule [Chain Rule]:
`\displaystyle (d)/(dx)[f(g(x))] =f'(g(x)) \cdot g'(x)`

eˣ Derivative:
`\displaystyle (d)/(dx) [e^u]=e^u \cdot u'`

Explanation:

Step 1: Define

`\displaystyle (d)/(dx)[e^(2x)]`

Step 2: Differentiate

1. [Derivative] eˣ Derivative [Chain Rule]:
   `\displaystyle (d)/(dx)[e^(2x)] = 2x^(1 - 1) \cdot e^(2x)`
2. [Derivative] Simplify:
   `\displaystyle (d)/(dx)[e^(2x)] = 2x^(0) \cdot e^(2x)`
3. [Derivative] Simplify:
   `\displaystyle (d)/(dx)[e^(2x)] = 2(1) \cdot e^(2x)`
4. [Derivative] Multiply:
   `\displaystyle (d)/(dx)[e^(2x)] = 2 \cdot e^(2x)`
5. [Derivative] Multiply:
   `\displaystyle (d)/(dx)[e^(2x)] = 2e^(2x)`

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Derivatives

Book: College Calculus 10e