Question

Differentiation:

Answer 1

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

Answer 2

perhaps you should expand the right side first.

Answer 3

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

Answer 4

Can't I just use the chain rule?

Answer 5

yes, just use the chain and product rule

Answer 6

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)

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

No, wait it would be -2x

Answer 12

thats correct
-2x

Answer 13

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. :)

Answer 14

welcome ^_^