# Derivative Problem

1. Sep 18, 2011

### 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.

2. Sep 18, 2011

### 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

3. Sep 18, 2011

### gb7nash

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

4. Sep 18, 2011

### Lancelot59

So I derived it correctly?

5. Sep 18, 2011

### Ray Vickson

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

RGV

6. Sep 18, 2011

### Lancelot59

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.