Math Problem Statement
Derivoi laskusäännöillä f (x) = (x 3 − e 2x ) (e −x + ln x)
Solution
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Math Problem Analysis
Mathematical Concepts
Differentiation
Product Rule
Exponential Functions
Logarithmic Functions
Formulas
Product Rule: f'(x) = u'(x) * v(x) + u(x) * v'(x)
Derivative of x^n: d/dx(x^n) = n*x^{n-1}
Derivative of e^{ax}: d/dx(e^{ax}) = a*e^{ax}
Derivative of ln(x): d/dx(ln(x)) = 1/x
Theorems
Product Rule
Power Rule
Exponential Function Derivative
Logarithmic Function Derivative
Suitable Grade Level
Undergraduate Calculus