Let y = (7/x^3)(√196x^6 +364x^2 + (169/x^2))
Find the derivative of y.
Hint: Simplify y before computing the derivative.
Answer: (-364/x^5)

Question

Let y = (7/x^3)(√196x^6 +364x^2 + (169/x^2))
Find the derivative of y.
Hint: Simplify y before computing the derivative.
Answer: (-364/x^5)

anonymous · Answer

does anyone know how to simplify the equation first before taking it's derivative?

anonymous · Answer

can you rewrite the equation using the equation tool on this site. It is tough to see in this form.

anonymous · Answer

yep

anonymous · Answer

$$y = \frac{ 7 }{ x^3 }\sqrt{196x^6 + 364x^2 + \frac{ 169 }{ x^2 }}$$

anonymous · Answer

Answer is $$\frac{ dy }{ dx } = \frac{ -364 }{ x^5 }$$

anonymous · Answer

I don't know how to simplify the radical. I would only know how to differentiate right away and it'll get messy

anonymous · Answer

ok thanks anyway

anonymous · Answer

you would use the product rule right?

anonymous · Answer

ya.

anonymous · Answer

I'm doing it too. it's getting pretty rough

anonymous · Answer

$$y' = -21x ^{-4} (196x^6 + 364x^2 + 169x^{-2})^{1/2} + 7x ^{-3}(\frac{ 1 }{ 2 } (196x^6 + 364 + 169x ^{-2})^{-1/2}(1176x^5 +728x -338x ^{-3})^{-1/2}$$

anonymous · Answer

whoops lol

anonymous · Answer

simplifying is the hardest part

zepdrix · Answer

Hmm there is something going on inside this square root, I'm trying to figure it out.
Not quite there yet, but I think it's not long off.
196 = 14^2
169=13^2

Hmmmm

zepdrix · Answer

OH! yes found it! :)

zepdrix · Answer

364 = 2 (13*14)

zepdrix · Answer

(14x^4 + 13)^2

I think it'll simplify like that.

anonymous · Answer

nice

anonymous · Answer

so how would this look like

anonymous · Answer

after simplifying?

zepdrix · Answer

|dw:1348968835510:dw|
Hmm, I think it simplifies like this, looks much easier to deal with :)
I got lazy on the multiplying there hehe