# How do you use implicit differentiation to find #(d^2y)/(dx^2)# given #5=4x^2+5y^2#?

##### 1 Answer

Sep 4, 2016

See below.

#### Explanation:

Differentiate both sides of the equation.

I prefer to solve for

Now differentiate again

Now replace

Simplify

# = -4/5((y + (4x)/(5y))/y^2)#

# = -4/5((((y + (4x)/(5y)) * 5y))/(y^2 * 5y))#

# = -4/5 ((5y^2+4x^2)/(5y^3)) #

And we're kind of done except that in the original statement of the question we're told that that numerator is