Derivative Problem: I'm Unsure of My Work

[Lancelot59]

I'm unsure of my work when completing this problem:

$$y=e^{-x^{2}} \int^{x}_{0} e^{t^{2}} dt + c_{1}e^{-x^{2}}$$

I applied the product rule to the left bit.

$$\frac{dy}{dx}=e^{-x^{2}} e^{x^{2}} + e^{-x^{2}}(-2x)\int^{x}_{0} e^{t^{2}} dt + (-2x)c_{1}e^{-x^{2}}$$

I'm fairly certain I did this wrong.

 

[JHamm]

I believe that:
$$\int^{x}_{0} e^{t^{2}} dt$$
Is a constant with respect to x, so you don't need to use the product rule, just treat it like any other constant

 

[gb7nash]

I believe that:
$$\int^{x}_{0} e^{t^{2}} dt$$
Is a constant with respect to x, so you don't need to use the product rule, just treat it like any other constant

No, this is a function with respect to x, so the product rule is valid here.

 

[Lancelot59]

So I derived it correctly?

 

[Ray Vickson]

I'm certain you did it right. Why do you think otherwise?

RGV

 

[Lancelot59]

I'm certain you did it right. Why do you think otherwise?

RGV

It's from a problem where I need to verify that it is a solution to:

$$y'+2xy=1$$

I was concerned that the integral still containing the "t" variable wouldn't cancel, however upon re-inspection I think it should.