Find the slope of the graph of y = ln(2x + 3 $) ^ { 1 / 2 }$ at the point (3, ln 3).
A) $\frac { \ln 3 } { 2 }$
B) $\frac { 1 } { \ln 3 }$
C) $\frac { 1 } { 2 ( \ln 3 ) + 3 }$
D) $\frac { 1 } { 9 }$

Question

Quizplus · Accepted Answer

To find the slope, differentiate y = ln((2x + 3)^(1/2)) using the chain rule: dy/dx = (1/(2x + 3)^(1/2)) * (1/2) * (2/(2x + 3)). Simplifying gives dy/dx = 1/(2x + 3). At x = 3, dy/dx = 1/9.

Find the Slope of the Graph of Y = Ln(2x )1/2) ^ { 1 / 2 })1/2

Find the Slope of the Graph of Y = Ln(2x $) ^ { 1 / 2 }$