Related Rates Calculus Tutorial

Let $y = \sin{(x)}$

Find $\frac{dy}{dt}$ when $x = \frac{\pi}{4}$ given $\frac{dx}{dt} = 2 \frac{cm}{sec}$

A 10 by 6 foot rectangular swimming pool is being filled. Find the rate at which the height of the water rises if the hose is pouring at $20 \frac{{ft}^3}{hour}$

A man 6 ft tall is walking away from a streetlight 20ft high at a rate of 5ft/sec. At what rate is the tip of his shadow moving when he is 24 feet from the lightpost and at what rate is the length of his shadow increasing?

A kite 100 ft above the ground moves horizontally at a speed of 8 ft/s. At what rate is the angle between the string and the horizontal decreasing when 200 ft of string has been let out?