Question

y= ln(e^(x^2-1) find y'(1)
a. 0
b. 1/2
c. 1
d. 2
e. undefined
PLEASE SHOW ALL STEPS THANK YOU!

Answer 1

(d)

Answer 2

\[\ln(e^{x^2-1}) = x^2-1\]
so
\[y=x^2-1\]
and
\[y'=2x\]
so y'(1) = 2.

Answer 3

ln(e^(x^2-1))=x^2-1, differentiate this and get dy/dx=2x, so at 1 dy/dx=2