Point $K$ is between points $J$ and $L$. If $J K=x^2-4 x, K L=3 x-2$, and $J L=28$, find $J K$ and $K L$.
$J K=$ $\square$ ,
$K L=$ $\square$

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.
;

Answered by Space | 2024-12-23