Partial Differentiation of Summations for Finding Derivatives

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To partially differentiate a summation for finding derivatives, the principle that the derivative of sums equals the sum of the derivatives is applied. The discussion centers on demonstrating that ∂/∂b₀ ƒ(b₀, b₁) equals -2 times the summation of the differences between observed values and predicted values. Participants seek clarification on how to effectively perform this differentiation step. The connection to foundational calculus concepts, such as the differentiation of sums, is emphasized. Understanding this process is crucial for solving related problems in calculus.
kerry michael
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Homework Statement



By differentiating the summation, show that ∂/∂b₀ ƒ(b₀ , b₁) = -2 ∑_(i=1)^n (y₁ - b₀ - b₁x₁)

Homework Equations



the ‘derivative of the sums’ equals ‘the sum of the derivatives’:



The Attempt at a Solution



How would we partially differentiate a summation in order to add up the derivatives which would find the derivative of the summation.??
 
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Way back in Calculus 1 you learned that (f+ g)'= f'+ g' didn't you?
 

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