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the derivative of y=sin(5x)cos(2x)
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1 Answer
Using product rule,
y'
= [sin(5x)]' cos(2x) + sin(5x)[cos(2x)]'
= 5cos(5x) cos(2x) - 2sin(5x) sin(2x)
Find the derivative of the function.
Using product rule,
y'
= [sin(5x)]' cos(2x) + sin(5x)[cos(2x)]'
= 5cos(5x) cos(2x) - 2sin(5x) sin(2x)
Comments
Thank you. I was wondering if you can go any farther and make it -2sin2 10x2 + 5cos2 10x2
- Lana M. from Leesburg, VA 11/25/2012It is tempting to go further, but since 5x and 2x are different arguments of cosine or sine you cannot combine them that way.
If you had an expression like 5 cos(2x)cos(2x) - 2 sin(5x)sin(5x) you would be able to combine to express it as 5 cos^2(2x) - 2 sin^2(5x).
- Jason T. 11/25/2012thank you so much! I understand now!
- Lana M. from Leesburg, VA 11/25/2012