Find \( \int \frac{1+x^{4}}{\left(1-x^{4}\right)^{3 / 2}} d x \)

K For the following composite function, find an inner function \( u=g(x) \) and an outer function \( y=f(u) \) such that \( y=f(g(x)) \). Then calculate \( y=\tan 3 x^{5} \) Identify the inner and outer functions. Choose the correct answer. A. \( u=g(x)=x^{5} \) and \( y=f(u)=3 \tan u \) B. \( u=g(x)=\tan x \) and \( y=f(u)=3 u^{5} \) O. \( u=g(x)=\tan x^{5} \) and \( y=f(u)=3 u \) \( \frac{d y}{d x}=\square \)

Determine the intervals on which the following function is concave up or concave down. Identify any inflection points. \( f(x)=x^{4}-3 x^{3}+9 \)

Determine the interval(s) on which the following function is continuous. \( f(x)=\frac{x^{2}-8 x+15}{x^{2}-9} \) The function is continuous on the interval(s) (Simplify your answer. Type your answer in interval notation. Use a comma to sepa

Find the intervals on which \( f \) is increasing and the intervals on which it is decreasing. \( f(x)=\frac{x^{4}}{4}-3 x^{3}+9 x^{2} \)

Given \( f(x, y)=3 x^{3}+x y^{2}-2 y^{6} \), find \( f_{y} \) \( 2 x-60 y \) \( 18 x \) \( 2 y \) None of these answers