How do you determine dy/dx given #x^(1/3)+y^(1/3)=7#?
1 Answer
May 13, 2017
Explanation:
Note that
The derivative with respect to
That is
So we have:
#x^(1/3)+y^(1/3)=7#
And taking the derivative of both sides:
#1/3x^(-2/3)+1/3y^(-2/3)dy/dx=0#
Multiplying both sides by
#1/x^(2/3)+1/y^(2/3)dy/dx=0#
Solving for
#1/y^(2/3)dy/dx=-1/x^(2/3)#
#dy/dx=-y^(2/3)/x^(2/3)=-(y/x)^(2/3)#