- #1
justin345
- 15
- 0
Homework Statement
e3x(3sin x-cos x)
The Attempt at a Solution
e3x3(3sin x-cos x)+(3cos x+sin x)e3x=10e3xsin x.
Is that right?
justin345 said:Homework Statement
e3x(3sin x-cos x)
The Attempt at a Solution
e3x3(3sin x-cos x)+(3cos x+sin x)e3x=10e3xsin x.
Is that right?
justin345 said:OK, so let me then get rid of parenthesis. I will show you my intermediate steps.
e3x3sinx-e3xcosx=
3e3xsinx+e3x3cosx-(3e3xcosx+e3x(-sinx))=
10e3xsin x
lurflurf said:Don't worry about berkeman's confusing, unclear, and not helpful post. Your work is quite correct, but it may help to use a few more steps until you have more practice.
Both rules need to be used in this problem. The product rule is used first, because the function is a product - e3x(3sin x-cos x). Then, to differentiate e3x, the chain rule is called for.berkeman said:Sorry if I was confusing. Should I have been using the term product rule instead of the more general chain rule? It was the intermediate steps that I was trying to get laid out.
Distributing the e term first refers to the mathematical process of multiplying the term e (a mathematical constant approximately equal to 2.718) by the terms inside a set of parentheses before multiplying them by any other terms outside the parentheses.
Distributing the e term first is important because it follows the mathematical rules of order of operations, which dictate that parentheses must be evaluated first. By distributing the e term first, the expression is simplified and can be solved correctly.
The steps for distributing the e term first are:1. Identify the terms inside the parentheses.2. Multiply each of these terms by e.3. Simplify the expression by combining like terms, if necessary.4. Multiply the remaining terms outside the parentheses by the simplified expression from step 3.
No, the e term can only be distributed first in expressions that contain parentheses. Additionally, the e term can only be distributed if it is being multiplied by the terms inside the parentheses.
Yes, one exception is when the expression inside the parentheses is already in the form of e^x, where x is a number. In this case, the e term does not need to be distributed and can be left as is.