Question

Calculus- derivatives.

I have two questions i need help with. My teacher told me i got a part of each answer wrong. Can someone please tell me which part and what the answer is.

First one:
-22x^-5 - 17x^-11/ 21x^-4 = 22x^-2/21 + 17x^-8/3.

Second one:
7x^2+5x^9/4x^7= 5x/2- 35/4x^6

Answer 1

Kinda hard to read. Show the original question as a screenshot.

Answer 2

Its numbers 3 and 4. I got the other ones correct.

Answer 3

Are you there?

Answer 4

You know that when we are multiply two terms with the same bases, we just sum the exponents or the powers.
So when you are going to to this, it will be like this:
\[\frac{ -22x^{-5}-17x^{-11} }{ 21x^{-4} }=\frac{ -22x^{-5} }{ 21x^{-4} }-\frac{ -17x^{-11} }{ 21x^{-4} }\]
\[=\frac{ -1.0476 }{ x }-\frac{0.8095 }{ x^7 }\]

Answer 5

Are you finding derivatives of 3 and 4? First simplify them, then find the derivative.\[\Large \frac{ -22x^{-5} -17x^{-11}}{ 21x^{-4} } = -\frac{ 22 }{ 21 }x^{-1} -\frac{ 17 }{21 }x^{-7}\]Now use the power rule to simplify the derivative of\[\Large -\frac{ 22 }{ 21 }x^{-1} -\frac{ 17 }{21 }x^{-7}\]

Answer 6

and for number 4:
\[\frac{ 7x^2+5x^9 }{ 4x^7 }=\frac{ 7x^2 }{ 4x^7 }+\frac{ 5x^9 }{ 4x^7 }=\frac{ 1.75 }{ x^5 }+1.25x^2\]

Answer 7

Do you want the derivatives or just simplification?

Answer 8

Thanks for the medal!

But if you need their derivatives, just tell me.

Answer 9

I need the derivatives. Number three can not have any positive exponents in the answer.

Answer 10

So just use the power rule for derivatives.

Answer 11

If i do that for number 3, doesn't it still have negative exponents?

Answer 12

I have tried these two problems, and i can't figure them at all. I know how to do these type of problems but i can't find the right answer. I need the answers.

Answer 13

Derivative of\[\Large -\frac{ 22 }{ 21 }x^{-1} -\frac{ 17 }{21 }x^{-7} \]is\[\Large -\frac{ 22 }{ 21 }(-1)x^{-2} -\frac{ 17 }{21 }(-7)x^{-8}\](i left the simplifying to you)

Answer 14

Okay! I think I've figured out that answer to that one! What about number 4?

Answer 15

Deriv of\[ \large \frac{ 7 }{ 4 }x^{-5}+\frac{ 5 }{ 4 }x^2\]is\[ \large \frac{ 7 }{ 4 }(-5)x^{-6}+\frac{ 5 }{ 4 }(2)x \]

Answer 16

Thanks, agent0smith!
You are good at explanation.
You deserve a medal.

Answer 17

Thanks @3mar :)