Need help with some calculus homework; trig identites as well as bonus question.

[EETman]

Differentiate and simplify(use trig identities): z=(tan2θ+cot3θ)*(cos^²4θ+sin²4θ) and y=(e^2x)(3sin3x+2cos3x) (on these ones i am having some trouble getting them started, i am familiar but i was not in class on the day this was specifically explained)

Prove that (let a and b be positive real numbers): lim ((ab)^h-1)/h = lim ((a^h-1)/h) + lim ((b^h-1)/h)
prof was looking for an algebraic explanation, h->0 h->0 h->0
not just the rule that justifies it.


If you could show all applicable work/processes as well as the answers, it would be much appreciated!

Thanks!

 

[daon2]

Where are you having trouble? I can;t assess that from the work you've shown (none).

And as far as the proof, it can be as simple as ln(ab)=ln(a)+ln(b). You've given no information about what is expected of you.

 

[Deleted member 4993]

Differentiate and simplify(use trig identities): z=(tan2θ+cot3θ)*(cos^24θ+sin^24θ)

Is that:

z=(tan2θ+cot3θ)*(cos²4θ+sin²4θ)

or:

z=(tan2θ+cot3θ)*(cos²⁴θ+sin²⁴θ)


and y=(e^2x)(3sin3x+2cos3x)


Prove that: lim ((ab)^h-1)/h = lim ((a^h-1)/h) + lim ((b^h-1)/h)
h->0 h->0 h->0

If you could show all applicable work/processes as well as the answers, ...... We don't do that here! You show work - we show the next step.

it would be much appreciated!

Thanks!

Please share your work with us .

If you are stuck at the beginning tell us and we'll start with the definitions such as "what is commisson"?"

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...217#post322217

 

[EETman]

Apologies, i didnt notice the forum rules on the top. I clarified the superscripts of the first equation, didnt notice that it came out rather in-concise. I have completed all homework but due to extenuating circumstances i was not in class on this specific day and im not sure how to get them started and what rules specifically apply. Any and all help would be appreciated. Thanks.

 

[EETman]

one specific problem in having on the second question of the first part is as such: i figured the best way to solve would be using the chain rule so i broke it up as such; y=3sin3x+2cos3x and f(z)= e^2x(z), now the problem im running into is how to differentiate y.

 

[daon2]

one specific problem in having on the second question of the first part is as such: i figured the best way to solve would be using the chain rule so i broke it up as such; y=3sin3x+2cos3x and f(z)= e^2x(z), now the problem im running into is how to differentiate y.

You need to use the product rule first, or were you absent that day, too? No one has the time to give complete lessons.

Let \(\displaystyle f(x)=3\sin(3x) + 2\cos(3x)\), and let \(\displaystyle g(x) = e^{2x}\). Then differentiate \(\displaystyle f(x)g(x) = f'(x)g(x)+g'(x)f(x)\)

The chain rule tells us \(\displaystyle d/dx \ \sin(3x) = cos(3x)\cdot 3\).

 

[EETman]

You need to use the product rule first, or were you absent that day, too? No one has the time to give complete lessons.

Let \(\displaystyle f(x)=3\sin(3x) + 2\cos(3x)\), and let \(\displaystyle g(x) = e^{2x}\). Then differentiate \(\displaystyle f(x)g(x) = f'(x)g(x)+g'(x)f(x)\)

The chain rule tells us \(\displaystyle d/dx \ \sin(3x) = cos(3x)\cdot 3\).

which results in e^2x(9cos(3x)+6sin(3x))+2e^2x(3sin(3x)+2cos(3x)) right?

 

[fcabanski]

which results in e^2x(9cos(3x)+6sin(3x))+2e^2x(3sin(3x)+2cos(3x)) right?

The derivative of cos is (-sin). So your derivative for that portion is not correct.