Math Problem Statement

Find the derivative of the function. yequals=4 x e Superscript negative 3 x Baseline minus 2 e Superscript x Super Superscript 4xe^(−3x)−2e^(x)^(4)

Solution

We are given the function:

y=4xe−3x−2ex4y = 4xe^{-3x} - 2e^{x^4}

Step 1: Derivative of 4xe−3x4xe^{-3x}

We use the product rule for the term (4xe^{-3x

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Math Problem Analysis

Mathematical Concepts

Calculus
Differentiation
Product Rule
Chain Rule
Exponential Functions

Formulas

Product rule: (uv)' = u'v + uv'
Chain rule: (f(g(x)))' = f'(g(x)) * g'(x)
Derivative of e^(ax): (d/dx) e^(ax) = ae^(ax)

Theorems

Product Rule for differentiation
Chain Rule for composite functions

Suitable Grade Level

College-level Calculus

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