I don't understand how to solve this problem

Please someone help me with the question

Yuki888 [10]

Answer:

$\displaystyle \frac{d}{dx}[e^{2x}] = 2e^{2x}$

$\displaystyle \frac{d}{dx}[e^{3x}] = 3e^{3x}$

General Formulas and Concepts:

Algebra I

Terms/Coefficients
Exponential Rule [Multiplying]: $\displaystyle b^m \cdot b^n = b^{m + n}$

Calculus

Derivatives

Derivative Notation

eˣ Derivative: $\displaystyle \frac{d}{dx}[e^x] = e^x$

Derivative Rule [Product Rule]: $\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)$

Step-by-step explanation:

Step 1: Define

$\displaystyle \frac{d}{dx}[e^{2x}] = \frac{d}{dx}[e^x \cdot e^x]$

$\displaystyle \frac{d}{dx}[e^{3x}] = \frac{d}{dx}[e^x \cdot e^{2x}]$

Step 2: Differentiate

$\displaystyle \frac{d}{dx}[e^{2x}]$

[Derivative] Product Rule: $\displaystyle \frac{d}{dx}[e^{2x}] = \frac{d}{dx}[e^x]e^x + e^x\frac{d}{dx}[e^x]$
[Derivative] eˣ Derivative: $\displaystyle \frac{d}{dx}[e^{2x}] = e^x \cdot e^x + e^x \cdot e^x$
[Derivative] Multiply [Exponential Rule - Multiplying]: $\displaystyle \frac{d}{dx}[e^{2x}] = e^{2x} + e^{2x}$
[Derivative] Combine like terms [Addition]: $\displaystyle \frac{d}{dx}[e^{2x}] = 2e^{2x}$

$\displaystyle \frac{d}{dx}[e^{3x}]$

[Derivative] Product Rule: $\displaystyle \frac{d}{dx}[e^{3x}] = \frac{d}{dx}[e^x]e^{2x} + e^x\frac{d}{dx}[e^{2x}]$
[Derivative] eˣ Derivatives: $\displaystyle \frac{d}{dx}[e^{3x}] = e^x(e^{2x}) + e^x(2e^{2x})$
[Derivative] Multiply [Exponential Rule - Multiplying]: $\displaystyle \frac{d}{dx}[e^{3x}] = e^{3x} + 2e^{3x}$
[Derivative] Combine like terms [Addition]: $\displaystyle \frac{d}{dx}[e^{3x}] = 3e^{3x}$

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

Unit: Derivatives

Book: College Calculus 10e

8 0

3 years ago

X(8 + 2) + 3 = 2(5 + x) + 5(x + 1) − 6 A) −4 B) −2 C) 2 D) 4

gavmur [86]

$x(8+2)+3=2(5+x)+5(x+1)-6\\\\10x+3=10+2x+5x+5\\\\10x+3=7x+15\ \ \ |-3\\\\10x=7x+12\ \ \ |-7x\\\\3x=12\ \ \ \ |:3\\\\x=4$

Answer: D) 4

3 0

3 years ago

Ben, Cam, and Justin are lumberjacks. The number of trees they chop down is given by b+2c+3j, where b is the number of hours Ben

Rom4ik [11]

Answer: There are 26 trees which they chop down .

Explanation:

Since we have given that

the number of trees they chop down is given by

$b+2c+3j$

Where 'b' denotes number of hours Ben spends chopping,

'c' denotes number of hours Cam spends chopping,

'j' denotes number of hours Justin spends chopping.

Now, we have also given that,

Number of hours Ben spends chopping = 8

Number of hours Cam spends chopping = 3

Number of hours Justin spends chopping = 4

Now, we put the value of all these variable in the above expression ,we'll get

$8+2\times 3+3\times 4=8+6+12=26$

Hence, there are 26 trees which they chop down .

4 0

3 years ago

Read 2 more answers

What is 0,6,24,60,120,210 next number ?

Bess [88]

Answer: 336

Step-by-step explanation:

The numbers are all multiples of 6

6 0

3 years ago

Please help!! I don’t understand this.

Mama L [17]

You add all of them together if it’s labeled with a X.
For example, the first X is 1 hour. If it has 2 Xs it would be 2 hours, if no X is shown above, it’s zero hours.
Answer is 12 hours.

7 0

3 years ago