Lana M.

asked • 11/25/12

the derivative of y=sin(5x)cos(2x)

Find the derivative of the function. 

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Inactive Tutor answered • 11/25/12

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Using product rule,

y'

= [sin(5x)]' cos(2x) + sin(5x)[cos(2x)]'

= 5cos(5x) cos(2x) - 2sin(5x) sin(2x)

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Lana M.

Thank you. I was wondering if you can go any farther and make it -2sin2 10x2 + 5cos2 10x2

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11/25/12

Inactive Tutor

It 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).

 

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11/25/12

Lana M.

thank you so much! I understand now!

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11/25/12

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