Update public notes

Author: actions-user

content/杂七杂八/数学/数学分析3 大逃杀笔记2.md

@@ -290,7 +290,7 @@ $f在I无穷次可微\implies 有泰勒公式:f(x)=\sum^n_{k=0} \frac{f^{(k)}(x)
 
 ## 含参量积分
 
-常义含参积分
+### 常义含参积分
 
 ![[Pasted image 20251229195841.png]]
 
@@ -302,3 +302,9 @@ $f在I无穷次可微\implies 有泰勒公式:f(x)=\sum^n_{k=0} \frac{f^{(k)}(x)
 $$\frac{d}{dx}\left( \int ^{d}_{c} f(x,y)dy \right)=\int ^{d}_{c} \frac{\partial}{\partial x}f(x,y)dy$$
 
 
+**常义含参积分导数公式:**
+
+$$\frac{d}{dx}\int ^{\phi(x)}_{\rho(x)} f(x,y)dy=f(x,\phi(x))\cdot \phi'(x)-f(x,\rho'(x))+\int ^{\phi(x)}_{\rho(x)} \frac{\partial}{\partial x} f(x,y)$$
+
+### 广义含参积分
+