Kenneth S. answered • 10/17/16
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Assuming that my clarification of the problem is:
y = [x + (x + sin2x)3]7 then we take the derivative first by using the power rule & then by successive chain rule applications:
y'=7[x + (x + sin2x)3]6•
[1+3(x + sin2x]2•[1+2sinxcosx]
See later comments for a correction to be applied.
My clarifications were for the purpose of resolving the squaring associated with sin x...which could be ambiguous. (If sine of (x squared) had been intended, the squaring should have been within the argument parentheses)
Kenneth S.
Arturo, I just got back from session of bridge at the Chiangmai (Thailand) bridge club--that's why the multi-hour delay in responding to you.
At the point where I bring down the 3 from exponent and reduce power of (...) cubed to power 2, we then must go differentiate that which was inside, thus deriv. of x is 1, deriv. of sin2x is 2 sinxcosx...so that another entire factor. I think I did it correctly. RSVP
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10/17/16
Arturo O.
Kenneth, I see we are in very different time zones! (Who do you work for in Thailand?) Anyway, my question is, when you apply the chain rule and differentiate
x + (x + sin2x)3
it looks like it should give
1 + 3(x + sin2x)2(1 +2sinx*cosx)
instead of
[1 + 3(x + sin2x)2] (1 +2sinx*cosx).
Am I applying the rule incorrectly?
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10/17/16
Kenneth S.
OK, Arturo, I NOW (finally see) that I got lost in parenthesis land on this one.
I'm retired, and spend only about 4 months per year in USA. Am going back to the States and will resume in-person tutoring in February, through May. Then back home in Thailand, to amuse myself by free Answers (most of them correct, and many of them politically correct, but not all). Thanks.
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10/17/16
Arturo O.
Thank for for the reply, Kenneth. (By the way, that problem was posted earlier, I put up a solution, and made the same parenthesis mistake, so I deleted it. I think I will repost it as an edited update.)
On a separate subject, I am sure seeing a lot of junk math questions from Common Core (or at least what I suspect to be Common Core). There was a physics inclined plane problem where they gave both the dimensions of the right triangle and the inclination angle, but the angle was incompatible with the given dimensions. And there are problems where a student is told a speed given as x mph corresponds to a speed as y kph, but if you do the unit conversions, some are way off. This is very disturbing.
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10/17/16
Kenneth S.
Hi, Arturo: I can count on you, and a few other tutors, for excellent work, whenever we find well phrased questions. But the high incidence of poorly written questions is disheartening. In a way I am glad not to be in the high school classroom anymore, because the curriculum being imposed from outside forces is certainly creating stresses in good teachers. On the other hand, some part of me wants to get back into the fray, and to prevail (that's my Don Quixote side) in spite of all odds.
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10/17/16
Arturo O.
10/17/16