Question

derivative of sqt 2theta sin-theta

Answer 1

do you mean:
\[\sqrt{2\theta \sin(\theta)}\]

Answer 2

yes sir

Answer 3

What about the - in front of the "-theta"?

Answer 4

there is no negative

Answer 5

this is a simple question you can go about it in two ways most simple would be squaring

Answer 6

so square to take out the square root? which makes it the derivative of just 2thetasintheta u mean?

Answer 7

First we will rewrite it to:

[2(theta)sin(theta)]^1/2

Now we have to chain rule: the derivative of the outside will become:

1/2 [2(theta) sin(theta)]^-1/2 * d/d0 (2theta*sin(theta))

and the derivative inside, we will have to product rule:

2theta(cos(theta)) + 2sin(theta), all together we get:

1/2 [2(theta) sin(theta)]^-1/2 * 2(theta)cos(theta) + 2 sin(theta)

= 2(theta)cos(theta) + 2sin(theta) / 2[2(theta)sin(theta)]^1/2

Answer 8

where did u get the two sin theta? can u explain?

Answer 9

Solution attached

Answer 10

product rule: d/dx( f(x)*g(x) ) = f'(x)g(x) + f(x)g'(x)

if we let f(x) = 2(theta) and g(x) = sin(theta)

then d/dx ( f(x)*g(x) ) = d/dx (2(theta)) * sin(theta) + d/dx(sin(theta)) * 2(theta)

= 2*sin(theta) + cos(theta)*2(theta)
= 2sin(theta) + 2(theta)cos(theta)

Answer 11

@Hermeezey it would easier if you square then differentiate takes care of the square root

Answer 12

but the answer my professor has is what ipm1988 provided

Answer 13

which he did the square root to both sides and factoring the 2 out of the equation and taking the derivates then

Answer 14

@Dwade03 thats because you can factor out a 2 from the top, and it cancels with the 2 on the bottom.

@ipm1988 You would need to know about implicit differentiation to do that, and I didn't know if he/she learned that yet.

Answer 15

but would i get the answer wrong if i dnt factor out the 2 and leave it out as it is?

Answer 16

well math teachers always want you to simplify as much as possible, so if you can factor something out and reduce it, you probably should.

Answer 17

@Dwade03 there are many ways to do a question

Answer 18

thank you guys. very well much appreciated.. i am doing a review for my test but some of the answers the professor gave been wrong so which makes me confused about a lot of these problems.

Answer 19

@ipm1988 I am not that great when it comes to calculus so even a little tiny mistake i see will throw me off.

Answer 20

@Dwade03 do you think i was good at calculus no it took me some time and practise you would make mistakes in the start but with practise you would stop making those mistakes

Answer 21

Haha well I am trying not to make those mistake on my test...lol

Answer 22

@Dwade03 are you giving a test right now ?

Answer 23

Nooo man my test is in class on tuesday.

Answer 24

@Dwade03 tell what has your prof taught you and then perhaps i can tell you what you need

Answer 25

well our professor can be so confusing at times... we have gone over a whole chapter of derivatives from finding derivatives to implicit differentiation. but its very tough to understand what he is teaching because of his accent problems and the method of teaching which results in a very long process to solving problems.

Answer 26

are you familiar with chain rule

Answer 27

not really. but i know the product and quotient rule..

Answer 28

did you see the solution i gave you

Answer 29

yes sir

Answer 30

is chain rule the derivative of the function times the derivitive of the inside function?

Answer 31

yes plus i have solved this questions in another way see it it is different from what i used beofre and you would see that answer is same

Answer 32

this one is confusing

Answer 33

but do u see answers are same

Answer 34

yes...i did the way the other guy showed which is simpler according to me but i dnt know how to factor after i got 2sin(theta) + cos(theta) x 2(theta)

Answer 35

you cannot factor it