What is the derivative of #x=y^2#?
1 Answer
We can solve this problem in a few steps using Implicit Differentiation.
Step 1) Take the derivative of both sides with respect to x.
#(Delta)/(Deltax)(y^2)=(Delta)/(Deltax)(x)#
Step 2) To find

Chain rule:
#(Delta)/(Deltax)(u^n)= (n*u^(n1))*(u')# 
Plugging in our problem:
#(Delta)/(Deltax)(y^2)=(2*y)*(Deltay)/(Deltax)#
Step 3) Find

Power rule:
#(Delta)/(Deltax)(x^n)= (n*x^(n1))#

Plugging in our problem:
#(Delta)/(Deltax)(x)=1#
Step 4) Plugging in the values found in steps 2 and 3 back into the original equation (
#(2*y)*(Deltay)/(Deltax)=1#
Divide both sides by
#(Deltay)/(Deltax)=1/(2*y)#
This is the solution
Notice: the chain rule and power rule are very similar, the only differences are:
chain rule:
power rule: