How do you find the first and second derivative of y=e^(x^3)?

inhaltynuaddyh4b

inhaltynuaddyh4b

Answered question

2023-02-04

How to find the first and second derivative of y = e x 3 ?

Answer & Explanation

Corey Wise

Corey Wise

Beginner2023-02-05Added 9 answers

d d x e x 3 = 3 x 2 e x 3
d ( 2 ) d x 2 e x 3 = 6 x e x 3 ( 1 + 3 2 x 3 )
Explanation: Using the chain rule:
d d x e x 3 = d e x 3 d ( x 3 ) d ( x 3 ) d x = 3 x 2 e x 3
Then using the product rule:
d ( 2 ) d x 2 e x 3 = d d x ( 3 x 2 e x 3 ) = ( d d x 3 x 2 ) e x 3 + 3 x 2 ( d d x e x 3 ) = 6 x e x 3 + 3 x 2 3 x 2 e x 3 = 6 x e x 3 + 9 x 4 e x 3 = 6 x e x 3 ( 1 + 3 2 x 3 )

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?