Evaluate Integral: Find Derivative of Exp(-t^2)

[ehrenfest]

Homework Statement

How would you evaluate

$$\frac{d}{dx} \int _{x}^{tanx}exp(-t^2)dt$$ ?

Homework Equations

The Attempt at a Solution

So I think you want to substitute variables int order to get the lower limit a constant and the upper limit a variable with constant derivative. Then we just take out the derivative operator and the integral sign. I just cannot think of the right substitution...

 

[bel]

let $$\int exp(-t^2)dt = F(t)$$,

then, $$\int _{x}^{tanx}exp(-t^2)dt = F(tanx)-F(x)$$

then use the chain rule to differentiate, since you already know the derivative of $$F(x)$$.

 

[ehrenfest]

That works. Thanks.