What is the derivative of [tex]e^{2x}[/tex]?

\displaystyle \frac{d}{dx}[e^\big{2x}] = 2e^\big{2x}
General Formulas and Concepts:
Calculus
Differentiation

Derivatives
Derivative Notation

Derivative Property [Multiplied Constant]: d x d ​ [ c f ( x )] = c ⋅ f ′ ( x )
Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Derivative Rule [Chain Rule]: d x d ​ [ f ( g ( x ))] = f ′ ( g ( x )) ⋅ g ′ ( x ) ;

Answered by Space | 2024-06-24

The derivative of e 2 x is 2 e 2 x . This is calculated using the chain rule of differentiation. The process involves identifying the outer and inner functions and applying the derivative rules accordingly.
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Answered by Space | 2025-05-16