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Question 15Differentiate the function:V = In(sin 2r)BI4 HA4ITInectorioissnaG...

Question

Question 15Differentiate the function:V = In(sin 2r)BI4 HA4ITInectorioissnaG

Question 15 Differentiate the function: V = In(sin 2r) B I 4 HA 4 I T Inectorioissna G



Answers

Differentiate the function.
$ S(R) = 4\pi R^2 $

It's clear. So when you read here, So, yeah, we're gonna fund that derivative in terms of tea. So I wrote it a different way. I wrote it T plus four, and I put e in the numerator. It just becomes equal to D over d t 30 plus four e to the t you to the negative t terms T minus T plus or eat the negative t d over DT of tea. Fall over Tea Square. Then we've simplify this when we got t negative d over DT For tea comes T plus four. Eat the negative T plus one plus zero eat to the negative T minus T plus four e to the negative T crawl over Teeth Square. This becomes equal to t terms e to the negative T minus T plus four. Eat the negative T minus T plus four. Eat the negative T while over he's square, you simplify to get T square plus 14th plus four plus four times E to the negative t well over a T square

The given function is so far equals two fought by Uh huh. Artist square in discussion. We need to determine the derivative of the given function. So apply the differentiation rule on the given function and find the derivative as just a stash of r equals. Two Dubai idea of Fort by Are you square? Yeah. So it can be done s four by been declared by Dubai. They are off our square so it can be done as four by went to pride by two are so it equals to 45 are it is not quite

Hey, it's clear is the one you married here. So we're going to do are derivative. Do you ever Devi one over the square Less one over beach the fourth I'm very cute minus to be. Don't we get D over TV one over the square plus one over B to the fourth times. Be cubed minus to be was won over V square plus one over V to the fore de over de V Be cubed minus two V. This becomes equal to negative too. Three to the negative. Cute plus negative for beat the negative five comes V cubed minus two V plus three V Square minus two terms one times one over B Square plus one over V to the fourth simplify and we got B to the fourth plus be square plus six all over view to the fourth.

Oh, this problem gives you the formula for volume uh four thirds pi r cubed, in case you didn't know this is the formula for a volume of a sphere. Um But that's not the theme. And the problem theme. And the problem is that the to find the derivative, which if you're not familiar yet, D b d R is the same thing as the notation of the prime. Um But what we're gonna do is the derivative of a constant times are to the end power is equal to just multiplying the constant by the exponent and then subtract one from that exponent. Uh So I'm going to over explain this. Four thirds pi is part of the constant. Yes, your constant can be more than one number. Four thirds is one number, pi is one number, but it's representing one constant. So it's a multiply by moving that exponent in front And then subtract one from that exponent 3 -1 is two. Now I wouldn't let my students leave their answer like this because you can cancel out these threes. So the best answer for DVD R would be, or pi r squared


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