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3 years ago

What is the derivative of 3x+5x

Mathematics

1 answer:

Vaselesa [24]3 years ago

7 0

Answer:

$\displaystyle \frac{d}{dx}[3x + 5x] = 8$

General Formulas and Concepts:

<u>Calculus</u>

Differentiation

Derivatives
Derivative Notation

Derivative Property [Multiplied Constant]: $\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)$

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

$\displaystyle y = 3x + 5x$

<u>Step 2: Differentiate</u>

Simplify: $\displaystyle y = 8x$
Derivative Property [Multiplied Constant]: $\displaystyle y' = 8\frac{d}{dx}[x]$
Basic Power Rule: $\displaystyle y' = 8$

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

Unit: Differentiation

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Show work and explain with formulas:

Marina86 [1]

17 Answer: 205

<u>Step-by-step explanation:</u>

$\{1\dfrac{2}{3}+1\dfrac{5}{6}+2+...+8\dfrac{1}{3}\}\implies a_1=1\dfrac{2}{3},\ d=\dfrac{1}{6}\\\\\\a_n=a_1+d(n-1)\qquad solve\ for\ n\\\\8\dfrac{1}{3}=1\dfrac{2}{3}+\dfrac{1}{6}(n-1)\\\\\\\dfrac{25}{3}=\dfrac{5}{3}+\dfrac{1}{6}n-\dfrac{1}{6}\\\\\\\dfrac{50}{6}=\dfrac{10}{6}+\dfrac{1}{6}n-\dfrac{1}{6}\\\\\\\dfrac{41}{6}=\dfrac{1}{6}n\\\\\\\dfrac{41}{6}\cdot 6=n\\\\41=n$

$\text{Now use the sum formula:}\\\\S_n=\dfrac{a_1+a_n}{2}\cdot n\\\\\\S_{41}=\dfrac{1\dfrac{2}{3}+8\dfrac{1}{3}}{2}\cdot 41\\\\\\.\quad =\dfrac{10}{2}\cdot 41\\\\\\.\quad =5\cdot 41\\\\.\quad =\large\boxed{205}$

18 Answer: 1968

<u>Step-by-step explanation:</u>

$a_1=-6,\ d=2,\ n=48, \quad \text{solve for }a_{48}\\\\a_{n}=a_1+d(n-1)\\\\a_{48}=-6+2(48-1)\\\\.\quad =-6+2(47)\\\\.\quad =-6+94\\\\.\quad =88$

$\text{Now use the sum formula:}\\\\S_n=\dfrac{a_1+a_n}{2}\cdot n\\\\\\S_{48}=\dfrac{-6+88}{2}\cdot 48\\\\\\.\quad =\dfrac{82}{2}\cdot 48\\\\\\.\quad =41\cdot 48\\\\.\quad =\large\boxed{1968}$

19 Answer: -116

<u>Step-by-step explanation:</u>

$\{3, -2, -7, ...\}\\a_1=3,\ d=-5,\ n=8, \quad \text{solve for }a_{8}\\\\a_{n}=a_1+d(n-1)\\\\a_{8}=3-5(8-1)\\\\.\quad =3-5(7)\\\\.\quad =3-35\\\\.\quad =-32\\\\\text{Now use the sum formula:}\\\\S_8=\dfrac{a_1+a_8}{2}\cdot 8\\\\\\S_{8}=\dfrac{3-32}{2}\cdot 8\\\\\\.\quad =\dfrac{-29}{2}\cdot 8\\\\\\.\quad =-29\cdot 4\\\\.\quad =\large\boxed{-116}$

6 0

3 years ago

Find the 10th term of the sequence defined by the rule, f (n) = 4n - 3.

DiKsa [7]

Answer:

Step-by-step explanation:

f(n) = 4n - 3

f(10) = 4×10 - 3 = 40 - 3 = 37

6 0

3 years ago

PLEASE ANSWER FAST I WILL GIVE BRAINLIEST

ANTONII [103]

Answer: 10 units²

Step-by-step explanation:

We can divide the shape along the y-axis to get 2 separate triangles. If we find the area of each and add them up, we can get the total area of the figure.

We can get each triangle's area using the formula $A = \frac{1}{2}bh$

<h3>Left Triangle</h3>

base length - 4 units

height - 4 units

$A = \frac{1}{2}(4)(4)$

$A=\frac{1}{2}(16)$

$A =8\hspace{0.1cm}units^2$

<h3>Right Triangle</h3>

base length - 2 units

height - 2 units

$A = \frac{1}{2}(2)(2)$

$A=\frac{1}{2}(4)$

$A=2\hspace{0.1cm}units^2$

Total = 8 units² + 2 units² = 10 units²

6 0

1 year ago

In a basketball game, a regular basket was worth 2 points and a long-distance basket was worth 3 points. if there were 45 basket

IgorLugansk [536]

Let
x: number of regular basketball
y: number of long-distance basket
We have the following system of equations:
2x + 3y = 96
x + y = 45
Solving the system we have
y = 45-x
2x + 3 (45-x) = 96
2x +135 -3x = 96
-x = 96 -135
x = 39
Then,
y = 45-x
y = 45-39
y = 6
answer
were made
regular baskets = 39
long-distance baskets = 6

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3 years ago

HELP URGENT!!!!

Vikki [24]

The equation should be y= -2x+5.

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3 years ago