Deriva 10 siguiente \( \left(3 x^{2}+6 x\right)\left(5 x^{2}+3 x\right) \)

Find the integral by the simplest method. \( \int 6 x \cos (2 x) d x=\square \)

During the time interval \( 0 \leq t \leq 6 \), the rate at which the amount of water in a tank is changing, in liters per minute, can be modeled by the function \( E(t)=49 \sin \left(0.11 t^{2}\right)+17 \), where \( t \) is measured in minutes. What is the average rate of change of the function \( E(t) \) from time \( t=0 \) to time \( t=6 \) ? You may use a calculator and round to the nearest thousandth. Indicate units of measure.

El volumen del sólido limitado superiormente por \( z=x^{2}+y^{2} \) e inferiormente por la región \( R=\{(x, y),|x| \leq 1,|y| \leqslant 1\} \) es: (A) \( \frac{8}{3} u^{3} \) (B) \( \frac{7}{3} u^{3} \) (C) \( \frac{5}{3} u^{3} \) (D) \( \frac{4}{3} u^{3} \)

Find the derivative of the given function. \( f(x)=\tanh ^{-1}(4 x) \) \( f^{\prime}(x)=\square \)

El volumen del sólido limitado superiormente por el paraboloide \( z=2-x^{2}-y^{2} \) e inferiormente por el plano \( 2 z=1 \) es: (A) \( \frac{9}{8} \pi u^{3} \) (B) \( \frac{7}{8} \pi u^{3} \) (C) \( \frac{5}{8} \pi u^{3} \) (D) \( \frac{3}{8} \pi u^{3} \)