Differences

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--- chain_rules [2026/03/10 22:02] – [e.g.] hkimscil
+++ chain_rules [2026/05/05 23:18] (current) – [Chain rules] hkimscil
@@ Line 9: / Line 9: @@
 \therefore{ \;\; } \frac {dy}{dx} & = & f'(g(x)) * g'(x) \\
 \end{eqnarray*}
+how to read dy/dx :
+  * derivation of y with respect of x
+  * y를 x에 대해서 미분
+따라서 위는
+  * y를 t에 대해서 미분하고
+  * t를 x에 대해서 미분한다 라고 읽는다
 ====== E.g ======
@@ Line 45: / Line 52: @@
 \text{a} & = & \text{intercept} \\
 \text{residual} & = & (y - \widehat{y}) \\
-\dfrac{\text{d.[SSR]}^2}{\text{d.a}} & = &
+\text{SSR} & = & \sum  {\text{residual}^2} = \sum{(y - (a + b x))^2}  \\
-\dfrac{\text{d.[SSR]}^2}{\text{d.Res}} * \dfrac{\text{d.Res}}{\text{d.a}} \\
+\dfrac{\text{d.SSR}}{\text{d.a}} & = &
+\dfrac{\text{d.SSR}}{\text{d.Res}} * \dfrac{\text{d.Res}}{\text{d.a}} \\
 & = & (2 * \text{residual}) * \dfrac{ \text{d.Res}} {\text{d.intercept}} \\
 & = & (2 * \text{residual}) * \dfrac{y - (a + b * x)} {\text{d.intercept}} \\
@@ Line 60: / Line 68: @@
 \text{b} & = & \text{slope} \\
 \text{residual} & = & (y - \widehat{y}) \\
-\dfrac{\text{d.[SSR]}^2}{\text{d.a}} & = &
+\text{SSR} & = & \sum  {\text{residual}^2} = \sum{(y - (a + b x))^2}  \\
-\dfrac{\text{d.[SSR]}^2}{\text{d.Res}} * \dfrac{\text{d.Res}}{\text{d.b}} \\
+\dfrac{\text{d.SSR}}{\text{d.a}} & = &
+\dfrac{\text{d.SSR}}{\text{d.Res}} * \dfrac{\text{d.Res}}{\text{d.b}} \\
 & = & (2 * \text{residual}) * \dfrac{ \text{d.Res}} {\text{d.b}} \\
 & = & (2 * \text{residual}) * \dfrac{y - (a + b * x)} {\text{d.b}} \\
 & = & 2 * \text{residual} * -x \\
-& = & -2 * x * \text{residual} \\
+& = & -2 x * \text{residual} \\
-& = & -2 * x * (y - (a + b * x)) \\
+& = & -2 x * (y - (a + b * x)) \\
-& = & -2 * x * (y - \widehat{y}) \\
+& = & -2 x * (y - \widehat{y}) \\
 \end{eqnarray*}