How do you use implicit differentiation to find the slope of the curve given #x^(1/4)+y^(1/4)=4# at (16,16)?

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Answer 1 · 2017-02-02T01:37:27

#-1#.

#1/4x^(-3/4) + 1/4y^(-3/4)(dy/dx) = 0#

#1/4y^(-3/4)(dy/dx)= -1/4x^(-3/4)#

#dy/dx = (-1/4x^(-3/4))/(1/4y^(-3/4))#

#dy/dx = -x^(-3/4)y^(3/4)#

#dy/dx = -y^(3/4)/(x^(3/4))#

Now simply evaluate the given point within the derivative.

#dy/dx = -(16^(3/4))/(16^(3/4))#

#dy/dx = -8/8#

#dy/dx = -1#

Hopefully this helps!