Describe the process of sketching a slope field for the differential equation \( y' = x + y \).

Use the quotient rule to take the derivative of the following functions: \( \begin{array}{ll}\text { 1. } y=\frac{x^{2}-4 x}{2 x+6} & \text { 2. } x+x y+y=2 \\ \text { 3. } y=x^{2} y+1 & \text { 4. } f(x)=\frac{\sqrt{x-1}}{\sqrt{3-x}}\end{array} \)

Consider the following. \[ y=\sinh \left(4-x^{2}\right),(2,0) \] Find \( y^{\prime} \) Find the slope of the line tangent to the graph of \( y \) at the given point. Find an equation of the tangent line to the graph of the function at the given point. .

Find an equation of the tangent line to the graph of the function at the point \( (1,1) \). \[ y=x^{\cosh (x)} \] \( y=\square \)

Evaluate the function. If the value is not a rational number, rouna (a) \( \operatorname{csch}^{-1}(3) \) (b) \( \operatorname{coth}^{-1}(6) \)

Find the derivative of the function. \[ y=\tanh \left(6 x^{2}-7\right) \] \( y^{\prime}=\square \)