Find the derivative of [tex]R = \left(100 + \frac{50}{\ln x}\right)[/tex].

R ′ = x ( ln x ) 2 − 50 ​
General Formulas and Concepts:
Calculus
Differentiation

Derivatives
Derivative Notation

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

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹


Derivative Rule [Quotient Rule]: d x d ​ [ g ( x ) f ( x ) ​ ] = g 2 ( x ) g ( x ) f ′ ( x ) − g ′ ( x ) f ( x ) ​ ;

Answered by Space | 2024-06-24

The derivative of the function R = 100 + l n x 50 ​ is R ′ = x ( l n x ) 2 − 50 ​ . This has been derived using the constant, and quotient rules of differentiation. Understanding this derivative is essential in many calculus applications.
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Answered by Space | 2024-12-23