# 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)#