Want site search autocompletion? See here Encountering 429 Too Many Requests errors when browsing the site? See here
Suppose f {\displaystyle f} is a function of two variables x , y {\displaystyle x,y} and f {\displaystyle f} and its partial derivative ∂ f / ∂ x {\displaystyle \partial f/\partial x} are both continuous functions on an interval of the form [ x 1 , x 2 ] × [ y 1 , y 2 ] {\displaystyle [x_{1},x_{2}]\times [y_{1},y_{2}]} . Then, for x ∈ ( x 1 , x 2 ) {\displaystyle x\in (x_{1},x_{2})} , we have:
d d x ∫ y 1 y 2 f ( x , y ) d y = ∫ y 1 y 2 ∂ ∂ x f ( x , y ) d y {\displaystyle {\frac {d}{dx}}\int _{y_{1}}^{y_{2}}f(x,y)\,dy=\int _{y_{1}}^{y_{2}}{\frac {\partial }{\partial x}}f(x,y)\,dy}
is a function of two variables 
and and its partial derivative 
are both continuous functions on an interval of the form ![{\displaystyle [x_{1},x_{2}]\times [y_{1},y_{2}]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6d7803853cc46b96eb756f1eb0087e6da87cc1d0)
. Then, for 
, we have:
