Question

HELP ASAP photo attached

Answer 1

Answer:

D. undefined

General Formulas and Concepts:

Calculus

Derivatives

Derivative Notation

Derivative of a constant is 0

Basic Power Rule:

• f(x) = cxⁿ
• f’(x) = c·nxⁿ⁻¹

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

Trig Derivative:                                                                                                       $\displaystyle \frac{d}{dx}[sinu] = u'cosu$

Derivatives of Parametrics:                                                                                   $\displaystyle \frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}}$

Step-by-step explanation:

Step 1: Define

$\displaystyle \frac{dx}{dt} = 5$

$\displaystyle \frac{dy}{dt} = sin(t^2)$

Step 2: Differentiate

1. [x Derivative] Basic Power Rule:                                                                   $\displaystyle \frac{d^2x}{dt^2} = 0$
2. [y Derivative] Trig Derivative [Chain Rule]:                                                 $\displaystyle \frac{d^2y}{dt^2} = cos(t^2) \cdot \frac{d}{dt}[t^2]$
3. [y Derivative] Basic Power Rule:                                                                   $\displaystyle \frac{d^2y}{dt^2} = cos(t^2) \cdot 2t^{2 - 1}$
4. [y Derivative] Simplify:                                                                                   $\displaystyle \frac{d^2y}{dt^2} = 2tcos(t^2)$
5. [Derivative] Rewrite:                                                                                     $\displaystyle \frac{d^2y}{dx^2} = \frac{2tcos(t^2)}{0}$

Anything divided by 0 is undefined.

Topic: AP Calculus BC (Calculus I/II)

Unit: Differentiation with Parametrics

Book: College Calculus 10e