- #1
chubbyorphan
- 45
- 0
Hey forum, thanks in advance to anyone who can explain this to me!
Find the derivative of each of the following:
h(x) = 3e^sin(x + 2)
My friend and I worked through this together and solved for:
h’(x) = (3e^sin(x + 2))(cos(x + 2))
Using my graphing calculator I have already confirmed this answer..
What I need help with is just a little bit of light being shed on the concept..
My book says : the chain rule says the derivative of u^(-1) is (-1)u^(-2) u'
so I get that..
my book also says: the derivative of the function f(x)=a^g(x), where a is a positive constant, is given by f'(x)=a^g(x) lna g'(x)
so applying to the question above.. isn't 3e a positive constant..
so my question basically is.. when working this problem through..
is there a middle step where a 'lne' is established?
I realize lne = 1 anyway.. but I'm just wondering for the sake of making sure I thoroughly understand.
and if there is a middle step involving the natural logarithm(ln) why wouldn't it be ln3e
I realize its not because that would change the answer that I already confirmed but I'm just struggling to understand why not..
cuz if a mid step with ln is involved.. 3 * e is a positive constant I thought so I'd figure it would be ln3e :S
or another option is its lne * 3 which still equals 1..
anyway, I'm rambling now so if someone could please explain this to me I would really appreciate it!![Confused :confused: :confused:](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
Homework Statement
Find the derivative of each of the following:
h(x) = 3e^sin(x + 2)
The Attempt at a Solution
My friend and I worked through this together and solved for:
h’(x) = (3e^sin(x + 2))(cos(x + 2))
Using my graphing calculator I have already confirmed this answer..
Homework Equations
What I need help with is just a little bit of light being shed on the concept..
My book says : the chain rule says the derivative of u^(-1) is (-1)u^(-2) u'
so I get that..
my book also says: the derivative of the function f(x)=a^g(x), where a is a positive constant, is given by f'(x)=a^g(x) lna g'(x)
so applying to the question above.. isn't 3e a positive constant..
so my question basically is.. when working this problem through..
is there a middle step where a 'lne' is established?
I realize lne = 1 anyway.. but I'm just wondering for the sake of making sure I thoroughly understand.
and if there is a middle step involving the natural logarithm(ln) why wouldn't it be ln3e
I realize its not because that would change the answer that I already confirmed but I'm just struggling to understand why not..
cuz if a mid step with ln is involved.. 3 * e is a positive constant I thought so I'd figure it would be ln3e :S
or another option is its lne * 3 which still equals 1..
anyway, I'm rambling now so if someone could please explain this to me I would really appreciate it!