Question

find dy/dx= tan (2- theta) ?

Answer 1

do u sub

Answer 2

isn't the derivative of tan sec squared?

Answer 3

yes @11calcBC lol

Answer 4

lol just checking :D

Answer 5

then use the chain rule and ur done

Answer 6

if you want to show something, let tanx=sinx/cosx and use quotient rule

Answer 7

is 2-theta it's own u v?

Answer 8

\[\tan(2 - \theta)\]
this?

Answer 9

yes

Answer 10

Well, you start with the derivative of the outermost thing and work your way inward. Everytime you take the derivative of something deeper inside, you multiply the whole function by that derivative. So in this case you have 2 derivatives to take care of. The derivative of tan and the derivative of the inner portion, 2- theta. Chain rule requires that we take each of these derivatives and multiply them WITHOUT changing whats inside.

So we start off with the derivative of tangent, which is sec^2(theta). But again, we do not change the inside. So we have right now
\[\sec^{2}(2 - \theta)\]now this result gets multiplied by the derivative of 2 - theta. We treat theta like a variable, so when we take this derivative, 2 goes away and - theta just becomes -1. So this derivative simply results in a multiplication of -1, meaning our final answer is:
\[\frac{ dy }{ d \theta }= -\sec^{2}(2- \theta)\]

Answer 11

yayyyy! :D

Answer 12

GOT IT

Answer 13

for once lol

Answer 14

lol, long as itmakes sense xD

Answer 15

not sure what to so with the theyta within the problem r=theta sin theta ^(1/2) :( !

Answer 16

Is theta to the 1/2power or all of sin(theta)?

Answer 17

i think it would be just theta.. there's no parenthesis? :o

Answer 18

then we assume its to theta only. So I'll rewriteit for visual purposes:

\[\theta \sin( \theta^{1/2})\]So this means wehave product rule. So just to be organized, I can list all the components wehave

f(x) = theta
g(x) = sin( theta^1/2)
f'(x) = 1

and for g'(x), we treat it the same way we did with the previous problem. We take the derivative of the outermost thing first then work inside multiplying by each new derivative we take. So first is the sin part of it which just becomes cos( theta^1/2) now we go inside and work with that theta^1/2.
So by power rule, the 1/2 power comes down and then decreases by 1, leaving us with
\[\frac{ 1 }{ 2 } \theta^{-1/2}\], which then we multiply on to theprevious derivative, meaning g'(x) =
\[\frac{ 1 }{ 2 \sqrt{ \theta} }\cos( \sqrt{ \theta})\] Now if we put everything together into the product rule formula, we get:
\[\sin( \sqrt{\theta}) + \frac{ \theta}{2 \sqrt{ \theta}}\cos( \sqrt{ \theta}) \implies \sin(\sqrt{ \theta}) + \frac{ \sqrt{\theta}}{2}\cos( \sqrt{ \theta})\]

Answer 19

ahhhhhhhhhh! okay (:

Answer 20

got et lol

Answer 21

tysm!

Answer 22

yeah, np :3