Given the function y = 8e-²x² + 7 sec² 5x – 4 ln x³, find y'. Solution: y' = 4(3)x² x³3 +8(−4x)e-²x² +7(2) sec 5x (sec² 5x) (5) 12 -32xe -2x² y' + 70 sec² 5x tan 5x x +8(-2x²)(-4x)e¯ -2x² +7 (2) sec 5x (sec² 5x)(5) 64x³e-2x² + 140 sec³ 5x ==

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter2: Graphical And Tabular Analysis
Section2.1: Tables And Trends
Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...
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Given the function y = 8e-2x² + 7 sec² 5x – 4 ln x³, find y'.
Solution:
-2x²
y' =
4(3)x²
x3
+8(-4x)e-2
12
-2x²
y'
-32xe + 70 sec² 5x tan 5x
x
+8(−2x²)(−4x)e-2x² + 7(2) sec 5x (sec² 5x)(5)
64x³e-2x² + 140 sec³ 5x
+7 (2) sec 5x (sec² 5x)(5)
Transcribed Image Text:Given the function y = 8e-2x² + 7 sec² 5x – 4 ln x³, find y'. Solution: -2x² y' = 4(3)x² x3 +8(-4x)e-2 12 -2x² y' -32xe + 70 sec² 5x tan 5x x +8(−2x²)(−4x)e-2x² + 7(2) sec 5x (sec² 5x)(5) 64x³e-2x² + 140 sec³ 5x +7 (2) sec 5x (sec² 5x)(5)
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