Question

PLEASE HELP!!! CALCULUS ASSIGNMENT

Answer 1

Answer:

(d)  $\displaystyle 12x^3 - 15x^2 + 2$

General Formulas and Concepts:

Algebra I

• Functions
• Function Notation

Calculus

Derivatives

Derivative Notation

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

Basic Power Rule:

• f(x) = cxⁿ
• f’(x) = c·nxⁿ⁻¹

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle y = 3x^4 - 5x^3 + 2x - 1$

Step 2: Differentiate

1. Basic Power Rule:                                                                                            $\displaystyle y' = 4(3x^{4 - 1}) - 3(5x^{3 - 1}) + 2x^{1 - 1} - 0$
2. Simplify:                                                                                                             $\displaystyle y' = 4(3x^3) - 3(5x^2) + 2$
3. Multiply:                                                                                                             $\displaystyle y' = 12x^3 - 15x^2 + 2$

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

Unit: Derivatives

Book: College Calculus 10e

Answer 2

Answer:

( d ) 12x³ - 15x² + 2

Step-by-step explanation:

y = 3x⁴ - 5x³ + 2x - 1

• The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of axⁿ is nax^{n-1}.

$\small \sf \: y = 4\times 3x^{4-1}+3\left(-5\right)x^{3-1}+2x^{1-1}$

• multiply 4 × 3.

$\small \sf \: y = 12x^{4-1}+3\left(-5\right)x^{3-1}+2x^{1-1}$

• Multiply 3 × -5

$\small \sf \: y = 12x^{3}-15x^{3-1}+2x^{1-1}$

• subtract the exponents

y = 12x³ - 15x² + 2⁰

• For any term t except 0, t⁰ = 1.

y = 12x³ - 15x² + 2 × 1

y = 12x³ - 15x² + 2

Hence, option ( d ) is the correct answer.