Find the second derivative of y from the equation 4x^2+8y^2 = 36.

Question

CALCULUS. DERIVATIVES. Need help for this , appreciated it if you guys respond. Thank You.

Answer 1

To find the derivative of y, we use the chain rule.  Take the derivative of the inside function and multiply it by the derivative of the outside function evaluated inside.  The inside function is the part of the function you would normally calculate first.

 

y' = -x(1/2)(-1/2x² + 9/2)^-1/2

 

y' = (-1/2)x(-1/2x² + 9/2)^-1/2

 

 

Now we take the derivative of the result to find the second derivative.  Use a combination of product and chain rule.

 

y'' = (1/2)(-1/2x² + 9/2)^-1/2 + (1/2)x[-x(-1/2)(-1/2x² + 9/2)^-3/2]

 

 

Next, simplify the derivative and you are done.  I leave this part to you.

Answer 2

Hi Joshua,

 

I would start by dividing the entire equation by 8.  Then rearrange it in the form of y^2 =

Take the square root and you now have it in y=(9/2-1/2x^2)^1/2

for y' (first derivative) use substitution.

let u = 9/2-1/2x^2

so y' = (u)^(-1/2)du

du = -x, when taking the derivative of -1/2x^2

 

then apply same concept to find the second derivative