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Mathematics 24 Online
OpenStudy (lncognlto):

Differentiation:

OpenStudy (lncognlto):

Find dy/dx of \[y = (x + 2)^3(1 - \sin 2x)^2(1 + \tan x)^3\]

OpenStudy (solomonzelman):

perhaps you should expand the right side first.

OpenStudy (lncognlto):

So if y = fgh, then dy/dx = f'gh + fg'h + fgh'.

OpenStudy (lncognlto):

Can't I just use the chain rule?

hartnn (hartnn):

yes, just use the chain and product rule

OpenStudy (lncognlto):

So dy/dx = 3(x + 2)^2(gh) + (2(1 - sin 2x)(2 cos 2x))(fh) + (3(1 + tan x)^2 (sec^2 x))(fg)

OpenStudy (lncognlto):

Where f, g, and h are the undifferentiated functions.

hartnn (hartnn):

won't the middle term be - (2(1 - sin 2x)(2 cos 2x)) ?

hartnn (hartnn):

d/dx (1-sin 2x) = -2 cos 2x

OpenStudy (lncognlto):

That's the one part that's confusing me a little; doesn't dy/dx (1 - x^2) = 2x?

OpenStudy (lncognlto):

No, wait it would be -2x

hartnn (hartnn):

thats correct -2x

OpenStudy (lncognlto):

Okay, yeah, I see, then the middle term would be negative. Cool, thanks, I got it. I just wanted to check my answer, as I don't have a solution. :)

hartnn (hartnn):

welcome ^_^

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