# How do you find #(d^2y)/(dx^2)# for #2=2x^2-4y^2#?

##### 1 Answer

Feb 28, 2017

#### Explanation:

differentiate all terms on both sides

#color(blue)"implicitly with respect to x"#

#rArr0=4x-8y.dy/dx#

#rArrdy/dx=(-4x)/(-8y)=x/(2y)# The second derivative is obtained by differentiating

#dy/dx# differentiate

#dy/dx" using the " color(blue)"quotient rule"#

#rArr(d^2y)/(dx^2)=(2y.1-x.2dy/dx)/(4y^2)#

#color(white)(rArr(d^y)/(dx^2))=(2y-2x(x/(2y)))/(4y^2)#

#color(white)(rArr(d^2y)/(dx^2))=(2y-((x^2)/y))/(4y^2)#

#color(white)(rArr(d^2y)/(dx^2))=(2y^2-x^2)/(4y^3)#