How to Differentiate a Polynomial with Pi?

Thendi
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Homework Statement



y = -5x3 + 4/x5 + 1.7pi

Homework Equations



Differentiate each Function.
Derivatives

The Attempt at a Solution


I have done question like these before but this is the first time using pi.
I used all derivative rules none of them give me the right answer.
The answer I am suppose to get is -5(3x8 + 4)/x6
Grade 12 Calculus
 
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The Pi is a constant. It's derivative is zero. Now just work from there.
 


y = -5x^3 + 4/x^5 + 1.7pi
see how its like 4/x^5 how do you find the derivative of that.
I got the first part -15x^2+?
 


Thendi said:
y = -5x^3 + 4/x^5 + 1.7pi
see how its like 4/x^5 how do you find the derivative of that.
I got the first part -15x^2+?

4/x^5=4*x^(-5). Use the usual power rule.
 


ok I get -15x^2+4x^-5
i took out -5 as a common factor but the answer is -5(3x^8 + 4)/x^6
3x^8 where is the power of 8 coming from isn't it suppose to be 2
 


Thendi said:
ok I get -15x^2+4x^-5
i took out -5 as a common factor but the answer is -5(3x^8 + 4)/x^6
3x^8 where is the power of 8 coming from isn't it suppose to be 2

i) I said 4/x^5=4*x^(-5). You still need to differentiate it. ii) -5*3x^8/x^6=-15*x^2. They put an overall factor of x^6 into the denominator. Do you see?
 


-15x^2 minus 25x^-6 since (d/dx)5x^-5= (-5)(5)(x^-6) and -5x^3= (3)(-5)(x^2)
 


Thendi said:
ok I get -15x^2+4x^-5
i took out -5 as a common factor but the answer is -5(3x^8 + 4)/x^6
3x^8 where is the power of 8 coming from isn't it suppose to be 2

Setting aside the differentiation for a moment, when you say that you took out -5 as a common factor, you don't mean that you took it out of 4x^-5, do you? If so, this is not allowed. If not, ignore this post.
 


I am confused what does * mean? "i) I said 4/x^5=4*x^(-5). You still need to differentiate it." i did differentiate it...i get -20x^-6 is it right?
 
  • #10


oh i think you meant (-5x^3 plus 4)/(x^5) then this could be simplified to ((-5)/(x^2)) plus ((4)/(x^5)) where the derivative is (10/x^3 minus 25x^-6) since d/dx (-5x^-2)=(-2)(-5)(x^-3)
 
  • #11


Thendi said:
I am confused what does * mean? "i) I said 4/x^5=4*x^(-5). You still need to differentiate it." i did differentiate it...i get -20x^-6 is it right?

'*' mean multiply. You didn't say that in the original post. You said I get '-15x^2+4x^-5'. I get also get -15x^2-20x^(-6). You don't see how that's the same thing as -5(3x^8 + 4)/x^6??
 
  • #12


Robert1986 said:
Setting aside the differentiation for a moment, when you say that you took out -5 as a common factor, you don't mean that you took it out of 4x^-5, do you? If so, this is not allowed. If not, ignore this post.

no no i took -5 out of [-15x^2 - 20x-6]
so i get -5[3x^2 - 4x^-6]

~Dick
I am so confused, can you please do the whole question step by step if possible because I really need to know where I did the mistake. Anyone will do
 
  • #13


Thendi said:
no no i took -5 out of [-15x^2 - 20x-6]
so i get -5[3x^2 - 4x^-6]

I am so confused, can you please do the whole question step by step if possible because I really need to know where I did the mistake. Anyone

You haven't made any mistake. Except possibly in communication -15x^2-20x-6 is equal to -5(3x^8 + 4)/x^6 isn't it?
 
  • #14


oh I got the answer already.

Thanks a lot guys for the help especially Dick.
This is going to help me big time for my MCV.

I need to ask one more question before I sleep.
Thanks again. :P
 
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