chain rule
2007-09-21 18:37:29 · 3 answers · asked by lana 1 in Science & Mathematics ➔ Mathematics
Initial problem:
d/dx [ sin^39 x • cos^39 x ]
Product Rule:
cos^39 x • d/dx [ sin^39 x ] + sin^39 x • d/dx [ cos^39 x ]
Chain Rule:
cos^39 x •[ 39•sin^38 x•cos x ] + sin^39 x •[ 39•cos^38 x• -sin x ]
Simplification:
39 • cos^40 x • sin^38 x - 39 • sin^40 x • cos^38 x
2007-09-21 19:59:49 · answer #1 · answered by Anonymous · 0⤊ 0⤋
Differentiate (sin^39 x)(cos 39x).
Use the product rule and the chain rule.
d[(sin^39 x)(cos 39x)] /dx
= 39(sin^38 x)(cos x)(cos 39x) + (sin^39 x)[-39(sin 39x)]
= 39(sin^38 x)(cos x)(cos 39x) - 39(sin^39 x)(sin 39x)
= 39(sin^38 x) [(cos x)(cos 39x) - (sin x)(sin 39x)]
Notice the angle addition formula.
= 39(sin^38 x)(cos 40x)
2007-09-22 03:05:33 · answer #2 · answered by Northstar 7 · 0⤊ 0⤋
you really want sin(x) to the 39th power?
2007-09-22 01:46:36 · answer #3 · answered by cattbarf 7 · 0⤊ 0⤋