I'm having trouble with these two calculus exercises. The first one is a simple case of Integral differentiation. I have to differentiate:
$\int_x^b \frac{x}{1+t^2+\cos(t^2)}dt$
But sincerely I have no clue. I've been tempted to switch the limits of integration and put a minus in front of the integral, but that doesn't help me at all. What is that $x$ doing in that fraction?
The other one states:
Find $f^{(n)}(x)$ of the function $\frac{x^n}{1-x}$.
I know I have to find the nth derivative of the function but, as $n$ is present in the function, I'm confused. Does this mean that, if $n = 1$, I have to find the first derivative of $\frac{x^1}{1-x}$, if $n = 2$ find the second derivative of $\frac{x^2}{1-x}$ and so? I think that doesn't even make sense.
Thanks.