Çözüldü Derivative - Logarithm and Exponential Functions

From the University of British Columbia - CA:

https://i.ibb.co/J3N1xSQ/derivative.png
https://personal.math.ubc.ca/~loew/m100exam/sample1.pdf (Page 1, Question 8)
Answers or Solutions: https://personal.math.ubc.ca/~loew/m100exam/sample1soln.pdf

dy / y = -5dt ⇒ ln(y) = -5t ⇒ y = e^(-5t) ⇒ y^2 = z = e^(-10t)
f(z) = dz / dt = 2y·(dy / dt) = 2·[ e^(-5t) ]·[ -5·e^(-5t) ] = -10·[ e^(-10t) ] = -10z.