Evaluate the first derivative of the function below at (2, 2).

Two cars, one going due east at the rate of 90 km/hr and the other going due south at the rate of 60 km/hr, are traveling toward the intersection of two roads. At what rate are the cars approaching each other at the instant when the first car is 0.2 km and the second car is 0.15 km from the intersection?

Which of the following is the general solution of:

A ladder 7 m long is leaning against a wall. If the bottom of the ladder is pushed horizontally toward the wall at 1.5 m/s, how fast is the top of the ladder sliding up the wall when the bottom is 2 m from the wall?

Evaluate:

A whole roast chicken is taken from the oven when its temperature reached 185 degrees Fahrenheit. It is then placed on a table where the room temperature is 75 degrees Fahrenheit. After thirty minutes, the temperature of the viand is 150 degrees Fahrenheit. After 45 minutes more, what is the temperature of the roast chicken (in Fahrenheit)?

Evaluate the trigonometric function below from x = 1 up to x = 5.

The associated angles are in radians.

Find the general equation of the line tangent to the equation below at the given point. 

What is the coefficient of x in the equation of the tangent line?

What is the value of the derivative of the function below for x = 1? The given angle is in radians.

What is the value of the constant in the line tangent to the equation below at the given point? Consider the general form of the equation of the tangent line.