Calculate the integral of \( f(x, y)=\left(x^{2}+y^{2}\right)^{-2} \) over the region \( x^{2}+y^{2} \leq 25, x \geq \frac{5}{\sqrt{2}} \) by changing to polar coordinates. (Use symbolic notation and fractions where needed.) \( \iint_{D} f(r, \theta) d n d \theta=\square \) help fractions).

Suppose that \( f(x, y)=x^{4}+y^{4}-x y \). Then the minimum value of \( f(x, y) \) is.. A. -0.125 B. 0.125 C. 0 D. None of these answers

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

Find the derivative of the following function. \( g(t)=4 \sqrt{t} \) \( g^{\prime}(t)=\square \)

Find the derivative of the following function by first expanding the expression. \[ f(x)=(6 x+1)\left(5 x^{2}+7\right) \] \( f^{\prime}(x)=\square \)