How do you use implicit differentiation to find dy/dx given #ysqrt(x+1)=4#?

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Answer 1 · 2016-11-19T08:59:23

#dy/dx = (-4sqrt(x+1))/(x+1)^2#

#ysqrt(x+1) = 4#

#y*(x+1)^(-1/2) * 1 + (x+1)^(1/2) * dy/dx = 0# (Product Rule)

From the original equation: #y = 4/sqrt(x+1)#

Hence: #(x+1)^(1/2) * dy/dx = (-4)/sqrt(x+1) * (x+1)^(-1/2)#

#dy/dx = (-4)/(x+1) * 1/sqrt(x+1)#

#= (-4sqrt(x+1))/(x+1)^2#