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Please help ! I have been stuck on this calculus problems, I will mark you brainliest!​

Please Help I Have Been Stuck On This Calculus Problems I Will Mark You Brainliest class=

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Answer:

[tex]\displaystyle J'(3) = -1[/tex]

General Formulas and Concepts:

Algebra I

  • Functions
  • Function Notation

Calculus

Derivatives

Derivative Notation

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

Derivative:                                                                                                                     [tex]\displaystyle \frac{d}{dx} [e^u]=e^u \cdot u'[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle J(x) = e^{f(x)}[/tex]

Step 2: Differentiate

  1. eˣ Derivative [Derivative Rule - Chain Rule]:                                                  [tex]\displaystyle J'(x) = \frac{d}{dx}[e^{f(x)}] \cdot \frac{d}{dx}[f(x)][/tex]
  2. Simplify:                                                                                                             [tex]\displaystyle J'(x) = f'(x)e^{f(x)}[/tex]

Step 3: Evaluate

  1. Substitute in x [Derivative]:                                                                              [tex]\displaystyle J'(3) = f'(3)e^{f(3)}[/tex]
  2. Substitute in function values:                                                                          [tex]\displaystyle J'(3) = -e^{0}[/tex]
  3. Simplify:                                                                                                             [tex]\displaystyle J'(3) = -1[/tex]

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

Unit: Derivatives

Book: College Calculus 10e

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