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Numerade Educator

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Problem 11 Medium Difficulty

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

Answer

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

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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.