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3 years ago

F(x) = (x+3)(2x²+5) Find the derivative

Mathematics

1 answer:

morpeh [17]3 years ago

7 0

Answer:

f'(x) = 6x² + 12x + 5

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Distributive Property

Algebra I

Terms/Coefficients/Degrees

Calculus

Derivatives

Derivative Notation

Derivative of a constant is 0

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

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

f(x) = (x + 3)(2x² + 5)

Step 2: Differentiate

Product Rule [Basic Power Rule]: f'(x) = (1 · x¹⁻¹ + 0)(2x² + 5) + (x + 3)(2 · 2x²⁻¹ + 0)
[Derivative] Simplify: f'(x) = (1)(2x² + 5) + (x + 3)(4x)
[Derivative] Multiply: f'(x) = 2x² + 5 + (x + 3)(4x)
[Derivative] Distribute: f'(x) = 2x² + 5 + 4x² + 12x
[Derivative] Combine like terms: f'(x) = 6x² + 12x + 5

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I am Lyosha [343]

You have the right idea that things need to get multiplied.

What should be done is that the entire fraction needs to get multipled by the lowest common denominator of both denominators.

Let's look at the complex numerator. Its denominators are 5 and x + 6. Nothing is common with these, so both pieces are needed.

The complex denominator has x - 3 as its denominator. With nothing in common between it and the complex numerator, that piece is needed.

So we multiply the entire complex fraction by (5)(x + 6)(x -3).

Numerator: $(\frac{1}{5} -\frac{5}{x + 6})(5)(x +6)(x-3) =\frac{1}{5}(5)(x +6)(x-3) - \frac{5}{x + 6}(5)(x +6)(x-3)$

= (x+6)(x-3) - (5)(5)(x-3)

= (x+6)(x-3) - 25(x-3)

= (x-3)(x + 6 - 25) <--- by group factoring the common x - 3

= (x -3)(x - 19)

Denominator:

$\frac{25}{x - 3} * (5)(x + 6)(x - 3) = (25)(5)(x + 6) = 125(x + 6)$

Now we put the pieces together.

Our fraction simplies to (x - 3) (x - 19) / 125 (x + 6)

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3 years ago

What would have to be done to put 3x (2x - 7) =9 in standard form? Group of answer choices

Artemon [7]

Answer:

Step-by-step explanation:

3 0

2 years ago

Which equation is correct?

galben [10]

Answer:

4 (14.14=142=28)

Because 14 in 7 times-table, 142 in 7 times-table and 28 in 7 times-table.

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3 years ago

Read 2 more answers

Six years after a tree was planted, its height was 7 feet. Nine years after it was planted, its height was 16 feet. Which of the

pychu [463]

Considering that the grows at a constant rate we can form an equation where x = how many years after it was planted
and y = its height

Now we just need to find how many feet it grows each year. To do that we just need to compare its height from a certain age to another:
6 years after it was planted : 7 feet,
so x=6 and y = 7

9 years after it was planted: 16 feet
so x= 9 y=16

With thay we can conclude that in 3 years , the tree grew 9 feet. To discover how much the tree grow each year we just nee to divide 9 feet by 3 years which is 3 feet every year.

To write the equatopn now we just need to find the y-intercept which we can discover by setting x to 0:
If in 6 years after the tree was planted it is 7 feet long , we can discover how long it was when it was planted by subtracting 6 years of growth (The slope ) which is 3
7 - 6(years)×3(feet the tree grow each year)
7 - 18 = -11
The tree was -11 feet long when it was planted
which is our y-intercept
( I know it doesnt make sense , but if you apply to a graph it will make more sense )

Now we can make the equation
y = 3x -11

7 0

3 years ago

A random sample of bolts is taken from inventory, and their lengths are measured. The average length in the sample is 5.3 inches

LekaFEV [45]

Answer:

$L_x=5.3 inches$