Find the derivative of each function. $f(x)=\tanh x^{2}$

Solve the equation, where $0\leq x<2 \pi$. If the equation does not have an exact solution, round to the nearest hundredth of a radian.

$$\sin 2 x \sin x+\cos 2 x \cos x=1$$

Solve each trigonometric equation, where $0 \leq x<2 \pi$. If the equation does not have an exact solution, round to the nearest hundredth of a radian.

$$2 \sin ^2 x-\cos x-1=0$$

Predict the effect of increasing the temperature on the amounts of products in the following reactions:
(b) $\mathrm{C}(\mathrm{s})+\mathrm{H}_2 \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{CO}(\mathrm{g})+\mathrm{H}_2(\mathrm{~g}) \quad \Delta H_{\mathrm{rxn}}^{\circ}=131 \mathrm{~kJ}$

Convert the following angles to radian measure:

(a). $360^{\circ}$

(b). $45^{\circ}$

($c$). $-90^{\circ}$

(d). $30^{\circ}$

(e). $270^{\circ}$

(f). $-120^{\circ}$

(g). $225^{\circ}$

(h). $330^{\circ}$

Answer the following questions in complete sentences. Hay una torre en tu ciudad?

Find the derivative of the function. $y=3 \cot (n \theta)$

Determine two coterminal angles in radian measure (one positive and one negative) for each angle. (There are many correct answers). (a) $\frac{9 \pi}{4}$ (b) $-\frac{2 \pi}{15}$

Find the derivative y'(x). $\frac{y}{x+1}-3 y=\tan x$

Find the derivative of the given function. $f(x)=4^{-x}(x+1)$

Solve each trigonometric equation, where $0 \leq x<2 \pi$. If the equation does not have an exact solution, round to the nearest hundredth of a radian.

$$\cos^2 x-\cos x-2=0$$

Find the derivative of each function. $f(x)=\sqrt{\sinh x}$

Find the derivative of the function. $y=x^{2}+6 x-7$

Find the angles between the vectors to the nearest hundredth of a radian.

$$\mathbf { u } = \mathbf { i } + \sqrt { 2 \mathbf { j } } - \sqrt { 2 } \mathbf { k } , \quad \mathbf { v } = - \mathbf { i } + \mathbf { j } + \mathbf { k }$$