Which function represents the area with respect to time?

Mila has $420 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax. She buys a

aksik [14]

she can buy 3 out fitsStep-by-step explanation:

7 0

3 years ago

Factor the expression completely. 60x^3+50x^5

STatiana [176]

Answer: 10x^3(6+5x^2)

4 0

3 years ago

I’m not sure if I’m right but can someone help.!

loris [4]

Answer:

4/9

Step-by-step explanation:

because it is 0.44444444 repeating :)

6 0

3 years ago

Read 2 more answers

Please help me thanks

Dovator [93]

Answer:

It is 61 degress an acute angle.

Step-by-step explanation:

3 0

3 years ago

Find y' if y= In (x2 +6)^3/2 y'=

Schach [20]

Answer:

$\displaystyle y' = \frac{3xln(x^2 + 6)^{\frac{1}{2}}}{x^2 + 6}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Factoring

Calculus

Derivatives

Derivative Notation

Derivative of a constant is 0

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

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

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

ln Derivative: $\displaystyle \frac{d}{dx} [lnu] = \frac{u'}{u}$

Step-by-step explanation:

Step 1: Define

$\displaystyle y = ln(x^2 + 6)^{\frac{3}{2}}$

Step 2: Differentiate

[Derivative] Chain Rule: $\displaystyle y' = \frac{d}{dx}[ln(x^2 + 6)^{\frac{3}{2}}] \cdot \frac{d}{dx}[ln(x^2 + 6)] \cdot \frac{d}{dx}[x^2 + 6]$
[Derivative] Chain Rule [Basic Power Rule]: $\displaystyle y' = \frac{3}{2}ln(x^2 + 6)^{\frac{3}{2} - 1} \cdot \frac{d}{dx}[ln(x^2 + 6)] \cdot \frac{d}{dx}[x^2 + 6]$
[Derivative] Simplify: $\displaystyle y' = \frac{3}{2}ln(x^2 + 6)^{\frac{1}{2}} \cdot \frac{d}{dx}[ln(x^2 + 6)] \cdot \frac{d}{dx}[x^2 + 6]$
[Derivative] ln Derivative: $\displaystyle y' = \frac{3}{2}ln(x^2 + 6)^{\frac{1}{2}} \cdot \frac{1}{x^2 + 6} \cdot \frac{d}{dx}[x^2 + 6]$
[Derivative] Basic Power Rule: $\displaystyle y' = \frac{3}{2}ln(x^2 + 6)^{\frac{1}{2}} \cdot \frac{1}{x^2 + 6} \cdot (2 \cdot x^{2 - 1} + 0)$
[Derivative] Simplify: $\displaystyle y' = \frac{3}{2}ln(x^2 + 6)^{\frac{1}{2}} \cdot \frac{1}{x^2 + 6} \cdot (2x)$
[Derivative] Multiply: $\displaystyle y' = \frac{3ln(x^2 + 6)^{\frac{1}{2}}}{2} \cdot \frac{1}{x^2 + 6} \cdot (2x)$
[Derivative] Multiply: $\displaystyle y' = \frac{3ln(x^2 + 6)^{\frac{1}{2}}}{2(x^2 + 6)} \cdot (2x)$
[Derivative] Multiply: $\displaystyle y' = \frac{3(2x)ln(x^2 + 6)^{\frac{1}{2}}}{2(x^2 + 6)}$
[Derivative] Multiply: $\displaystyle y' = \frac{6xln(x^2 + 6)^{\frac{1}{2}}}{2(x^2 + 6)}$
[Derivative] Factor: $\displaystyle y' = \frac{2(3x)ln(x^2 + 6)^{\frac{1}{2}}}{2(x^2 + 6)}$
[Derivative] Simplify: $\displaystyle y' = \frac{3xln(x^2 + 6)^{\frac{1}{2}}}{x^2 + 6}$

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

Unit: Derivatives

Book: College Calculus 10e

3 0

3 years ago