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machine-learningneural-networkderivativequadratic
Peter234
Peter234

Reputation: 1052

How to correctly derivate quadratic cost function

Given the quadratic cost function f(a) = 1/2 (a-y)^2, I know that the derivative of the function with respect to a is a - y. But I have no clue how to get there... Can you provide me a link where this is explained easily?

Upvotes: 1

Views: 1763

Answers (1)

lejlot
lejlot

Reputation: 66805

Derivative in respect to what? Probably "a". Thus this is just about taking a derivative of a square of a difference.

f(a) = 1/2 (a-y)^2

df / da = d[ 1/2 (a-y)^2 ] / da
        = 1/2 d[ (a^2 -2ay + y^2) ] / da
        = 1/2 ( d[ a^2 ] / da - 2 d[ ay ] / da + d[ y^2 ] / da)
        = 1/2 ( 2a - 2y + 0 )
        = a - y

Upvotes: 5

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