💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Find the differential of each function.(a) $y = xe^{4x}$(b) $y = \sqrt {1 -t^4}$

(a) $(1-4 x) e^{-4 x} d x$(b) $d y=-\frac{2 t^{3}}{\sqrt{1-t^{4}}} d t$

Discussion

You must be signed in to discuss.
Anna Marie V.

Campbell University

Heather Z.

Oregon State University

Kristen K.

University of Michigan - Ann Arbor

Lectures

Join Bootcamp

Video Transcript

okay. Part A The derivative using the product rule. We have acts times You did the negative for ox Natural order of E. We know that we're taking the derivative of negative four acts. So in this case, this simplifies to negative for X E to the negative or ax plus e to the night of four ax using the chain rule and factoring we end up with Okay, Part B. We know that we have one nice t to the fourth to the 1/2. Therefore we have, if you have tea, is one nice to the fourth than we know that we could have 1/2 you to the negative. 1/2 comes negative for t cubed, which is negative to t cubed over the square root of one minus t to the fourth.