So it is given that f(x) and g(x) are inverse of each other.
Then f(5) = -7 and hence g(-7) = 5
Now let's use f( g( x ) ) = x
Now take deviation. Use chain rule:
f'( g(x) ) g'( x ) = 1
Plug in x = -7
f'( g( -7 ) ) g'( -7 ) = 1
f'( g( -7 ) ) · -2/3 = 1
f'( g( -7 ) ) = -3/2
f'( 5 ) = -3/2
Hope this helps.
Answer:
$2643.06
Step-by-step explanation:
Total purchase = $2436 + 8.5% of $2436
= $2436 + (0.085 * 2436)
= $2436 + $207.06
= $2643.06
Answer:
D. undefined
General Formulas and Concepts:
<u>Calculus</u>
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)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%28g%28x%29%29%5D%20%3Df%27%28g%28x%29%29%20%5Ccdot%20g%27%28x%29)
Trig Derivative: ![\displaystyle \frac{d}{dx}[sinu] = u'cosu](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bsinu%5D%20%3D%20u%27cosu)
Derivatives of Parametrics: 
Step-by-step explanation:
<u>Step 1: Define</u>


<u>Step 2: Differentiate</u>
- [x Derivative] Basic Power Rule:

- [y Derivative] Trig Derivative [Chain Rule]:
![\displaystyle \frac{d^2y}{dt^2} = cos(t^2) \cdot \frac{d}{dt}[t^2]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%5E2y%7D%7Bdt%5E2%7D%20%3D%20cos%28t%5E2%29%20%5Ccdot%20%5Cfrac%7Bd%7D%7Bdt%7D%5Bt%5E2%5D)
- [y Derivative] Basic Power Rule:

- [y Derivative] Simplify:

- [Derivative] Rewrite:

Anything divided by 0 is undefined.
Topic: AP Calculus BC (Calculus I/II)
Unit: Differentiation with Parametrics
Book: College Calculus 10e
You didn't provide more information regarding triangle but from given options, it seems that triangle has ratio from shortest side to longest side would be 5 : 12 : 13
So 13 would be hypotenuse since it is longest.
Now A cannot be right angle because tangent is not defined at 90°.
Also tan(A) would be ratio of opponent side to adjacent side (think SOH CAH TOA)
So either opposite side would be 5 or 12, and adjacent side would be 12 or 5 respectively.
So the answer is either 5 / 12 or 12 / 5 but only option provided is 12/5 so that would be your answer.
Final answer: 12 / 5
I would say... None.
Hope this helps ٩(๑❛▽❛๑)۶