Mathematics, 27.06.2019 13:30 arielgonzalez809

Find dy, dx if f(x) = (x + 8)3x. 3xln(x + 8) the product of the quantity 3 times the natural log of the quantity x plus 8 plus 3 times x divided by the quantity x plus 8, and the quantity x plus 8 raised to the 3x power 3 times the natural log of the quantity x plus 8 plus 3 times x divided by the quantity x plus 8 3x(x + 8)(3x − 1)

Answers: 1

Show answers

Answers

Answer from: NetherisIsTheQueen

$\displaystyle \frac{dy}{dx} = 3(x + 8)^{3x} \bigg[ \ln (x+ 8) + \frac{x}{x + 8} \bigg]$

General Formulas and Concepts:
Calculus

Differentiation

DerivativesDerivative Notation

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

Derivative Property [Addition/Subtraction]: $\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]$

Derivative Rule [Basic Power Rule]:

f(x) = cxⁿf’(x) = c·nxⁿ⁻¹

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

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

Step-by-step explanation:

Step 1: Define

Identify.

$\displaystyle f(x) = (x + 8)^{3x}$

Step 2: Differentiate

Exponential Differentiation [Derivative Rule - Chain Rule]: $\displaystyle \frac{dy}{dx} = (x + 8)^{3x} \frac{d}{dx} \bigg[ 3x \ln (x + 8) \bigg]$ Derivative Rule [Product Rule]: $\displaystyle \frac{dy}{dx} = (x + 8)^{3x} \bigg[ \frac{d}{dx}(3x) \ln (x + 8) + 3x \frac{d}{dx}[ \ln (x + 8)] \bigg]$ Rewrite [Derivative Property - Multiplied Constant]: $\displaystyle \frac{dy}{dx} = (x + 8)^{3x} \bigg[ 3 \frac{d}{dx}(x) \ln (x + 8) + 3x \frac{d}{dx}[ \ln (x + 8)] \bigg]$ Derivative Rule [Basic Power Rule]: $\displaystyle \frac{dy}{dx} = (x + 8)^{3x} \bigg[ 3 \ln (x + 8) + 3x \frac{d}{dx}[ \ln (x + 8)] \bigg]$ Logarithmic Differentiation [Derivative Rule - Chain Rule]: $\displaystyle \frac{dy}{dx} = (x + 8)^{3x} \bigg[ 3 \ln (x + 8) + \frac{3x}{x + 8} \frac{d}{dx} (x + 8) \bigg]$ Rewrite [Derivative Property - Addition/Subtraction]: $\displaystyle \frac{dy}{dx} = (x + 8)^{3x} \bigg[ 3 \ln (x + 8) + \frac{3x}{x + 8} \Big[ \frac{d}{dx}(x) + \frac{d}{dx}(8) \Big] \bigg]$ Derivative Rule [Basic Power Rule]: $\displaystyle \frac{dy}{dx} = (x + 8)^{3x} \bigg[ 3 \ln (x + 8) + \frac{3x}{x + 8} \bigg]$ Simplify: $\displaystyle \frac{dy}{dx} = 3(x + 8)^{3x} \bigg[ \ln (x+ 8) + \frac{x}{x + 8} \bigg]$

∴ we have found the derivative of the given function.

---

Learn more about derivatives: link

Learn more about calculus: link

---

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

Unit: Differentiation

Answer from: Quest

correct answer is infinitely many solutions

step-by-step explanation:

2(2x + 3) = -4 + 2(2x + 5)

solving the above equation:

4x + 6 = -4 +4x +10

combining like terms

4x -4x = -4+10-6

0=0

since both sides are 0=0, we end up into true statement it means it has infinite many solutions.

so correct answer is infinitely many solutions

Answer from: Quest

a is the correct

And do not get it wrong . this is a quiz and im struggling ! ☹️

Another question on Mathematics

Mathematics, 21.06.2019 15:00

1. a right triangle is graphed on a coordinate plane. find the length of the hypotenuse. round your answer to the nearest tenth. 2. use the angle relationship in the figure below to solve for the value of x. assume that lines a and b are parallel and line c is a transversal.

Answers: 1

Answer

Mathematics, 21.06.2019 22:10

2. using calculations based on a perpetual inventory system, determine the inventory balance altira would report in its august 31, 2021, balance sheet and the cost of goods sold it would report in its august 2021 income statement using the average cost method. (round "average cost per unit" to 2 decimal places.)

Answers: 1

Answer

Mathematics, 21.06.2019 23:00

The height of a birch tree, f(x), in inches, after x months is shown in the graph below. how much does the birch tree grow per month, and what will be the height of the birch tree after 10 months? a. the birch tree grows 1 inch per month. the height of the birch tree will be 16 inches after 10 months. b. the birch tree grows 2 inches per month. the height of the birch tree will be 26 inches after 10 months. c. the birch tree grows 3 inches per month. the height of the birch tree will be 36 inches after 10 months. d. the birch tree grows 2 inches per month. the height of the birch tree will be 24 inches after 10 months.

Answers: 1

Answer

Mathematics, 22.06.2019 02:30

There are three grizzly bears in the city zoo. yogi weighs 400.5 pounds, winnie weighs 560.35 pounds, and nyla weighs 628.29 pounds. what is the average weight of the three bears? (hint: what do they weigh all together? ) a. 502.97 pounds c. 604.38 pounds b. 529.71 pounds d. 794.57 pounds

Answers: 1

Answer

You know the right answer?

Find dy, dx if f(x) = (x + 8)3x. 3xln(x + 8) the product of the quantity 3 times the natural log of...

Questions