Finding the derivative of a multivariable integral? Okay so I'm asked to find $\frac{df}{dt}$ of $f(t)=\int_{1}^{t^2}{\frac{1}{s}e^{s^2t}ds}$. Letting $g(s)=\frac{1}{s}e^{s^2t}$ I get:
$$f'(t)=G'(t^2) \cdot 2t - G'(1) \cdot 0
=g(t^2) \cdot 2t = \frac{2}{t}e^{t^5} $$
I'm not sure where I'm going wrong here but I'm pretty sure it's incorrect. 

here 
$$\frac{d}{dt}\int_0^{b(t)}{f(s,t)\,ds}=f(b(t),t)\cdot b'(t)+\int_0^{b(t)}{\frac{\partial}{\partial t}f(s,t) ds}.$$
