Search
Ask a question
0

Differentiation Rules for Exponential Functions

how do you find the second derivative of y=e-x^2

1 Answer by Expert Tutors

Tutors, sign in to answer this question.
Philip P. | Effective and Affordable Math TutorEffective and Affordable Math Tutor
5.0 5.0 (443 lesson ratings) (443)
0
How do you find the second derivative of y=e-x^2
 
For the first derivative, use the chain rule:
 
Let u = -x2
 
y' = d(eu)/du * du/dx = eu*(-2x) = (-2x)e-x^2
 
For the second derivative use the chain rule and the product rule:
 
y'' = e-x^2*d(-2x)/dx + (-2x)d(eu)/du*(du/dx)
 
y'' = -2e-x^2 + 4x2e-x^2
 
y'' = 2e-x^2(2x2 - 1)