Shirley27
  • Shirley27
How would you take the second derivative of x^2 + 4y^2 =1 for x?
OCW Scholar - Single Variable Calculus
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
simplify it to be in the form: y = f(x) , then differentiate it
anonymous
  • anonymous
You could differentiate the whole equation: f'(x^2 + 4y^2 = 1) = (2x + 8y*y' = 0) 8y*y' = -2x => y'=-2x/8y and then differentiate again: y''=f'(-2x/8y) (using quotient rule): (-2*1*8y-(-2x*8y'))/(64y^2) = y'' (-16y+16xy')/(64y^2) = y'' (-4y+4x*(-2x/8y))/y^2 = y'' (-4y/y^2)+(-8x/8y^3) = y'' -4/y + x/y^3 = y'' whew. that feels wrong. This will likely be a learning experience for me as well! Thanks.
Shirley27
  • Shirley27
Thanks!!

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
Fairly sure now that this is wrong--if anyone would like to check my work, feel free and thank you.
anonymous
  • anonymous
the approach shulmand used is correct, but missed some accuracy. Here's the correct version. (using quotient rule): (-2*1*8y-(-2x*8y'))/(64y^2) = y'' (-16y+16xy')/(64y^2) = y'' (-4y+4x*(-2x/8y))/(16y^2) = y'' (-4y/16y^2)+(-8x^2/(16*8y^3)) = y'' -1/4y - x^2/16y^3 = y''
anonymous
  • anonymous
Thank you.

Looking for something else?

Not the answer you are looking for? Search for more explanations.