So i have the function $f(x,y) = \int_{0}^{x^2+y}t+e^{-t^2} dt$ which im supposed to find the partial derivates of.
Now after looking online i was able to solve this by using the leibniz rule. (Could be very wrong though)
$$\frac{\partial }{\partial x} = 2x-4xe^{-(x^2+y)^2}(x^2+y)$$
$$\frac{ \partial }{ \partial y } = 1-2e^{-(x^2+y)^2}(x^2+y)$$
Now the thing is, we havent covered the leibniz rule so im wondering if there are any other "easier" ways you can solve this or reason your way forward.
This has nothing to do with the Leibniz rule. The answers that you got follow from the chain rule and the fundamental theorem of Calculus.