(6) \( \lim _{t \rightarrow 0}\left(\frac{1}{t}-\frac{1}{t^{2}+t}\right) \)

Let \( f(x)=x^{2}+15 \), then \( f^{10}(x)= \) Let \( f(x)=\ln \left(x^{2}+1\right) \), then \( f^{\prime}(x)= \) Let \( f(x)=e^{\infty x} \), then \( f^{n}(x)= \)

What is the general solution to the following: \( \int 2 x \sin (x) d x \) ?

What is the solution to the differential equation \( \frac{d y}{d x}+x y=x, y(0)=-6 ? \)

A. The critical number of \( f(x) \) B. Find the intervals on which \( f \) is increasing and decreasing by using the first derivative test Find the local maximum and minimum, if they exist by using the first derivative test Find the intervals on which \( f \) is concave up and concave down Find the inflection points of \( f(x) \)

20. \( \int x \tan ^{2} x d x \)