- #1

chubbyorphan

- 45

- 0

## 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!