If the lesson or problem you are looking for isn’t on this list please send me an email to let me know about it at** jakesmathlessons@gmail.com**.

**Lessons about derivatives:**

**Lessons about derivatives:**

Finding Derivatives with Limits

The Product Rule

The Quotient Rule

The Chain Rule

How to find the equation of a tangent line

Linear Approximation (Linearization) and Differentials

Optimization Problems

Optimization Problems Part 2

Implicit Differentiation

Related Rates

**Extra problems about derivatives:**

**Extra problems about derivatives:**

Examples of product, quotient, and chain rules

**Solution** – Find two numbers whose sum is 23 and whose product is a maximum

**Solution** – Find the values of *a* and *b* that make the function differentiable everywhere

**Solution** – Find \(\frac{dy}{dx}\) if \(y=x^x\)

**Solution **– Find *dy/dx* by implicit differentiation examples

**Related rates problems:**

**Related rates problems:**

*Triangles*

**Solution** – At noon, ship A is *150 km* west of ship B. Ship A is sailing east at *35 km/h* and ship B is sailing north at *25 km/h*. How fast is the distance between the ships changing at 4:00 PM?

**Solution** – 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?

**Solution** – A plane flies horizontally at an altitude of *5 km* and passes directly over a tracking telescope on the ground. When the angle of elevation is \(\frac{\pi}{3}\), this angle is decreasing at a rate of \(\frac{\pi}{6} \ \frac{rad}{min}\). How fast is the plane traveling at this time?

**Solution **– The top of a ladder slides down a vertical wall at a rate of *0.15 *\(\frac{m}{s}\). At the moment when the bottom of the ladder is 3 *m* from the wall, it slides away from the wall at a rate of *0.2 *\(\frac{m}{s}\). How long is the ladder?

*Squares*

**Solution** – Each side of a square is increasing at a rate of *6 **cm/s*. At what rate is the area of the square increasing when the area of the square is *16 *\(cm^2\)?

**Cones**

**Solution** – Water is leaking out of an inverted conical tank at a rate of *10,000* \(\frac{cm^3}{min}\) at the same time water is being pumped into the tank at a constant rate. The tank has a height *6 m* and the diameter at the top is *4 m*. If the water level is rising at a rate of *20 *\(\frac{cm}{min}\) when the height of the water is *2 m*, find the rate at which water is being pumped into the tank.

**Spheres**

**Solution** – If a snowball melts so that its surface area decreases at a rate of *1 *\(\frac{cm^2}{min}\), find the rate at which the diameter decreases when the diameter is *10 cm*.

**Solution** – The radius of a sphere is increasing at a rate of *4 *\(\frac{mm}{s}\). How fast is the volume increasing when the diameter is *80 mm*?

*Cylinders*

**Solution** – A cylindrical tank with radius *5 m* is being ﬁlled with water at a rate of *3 *\(\frac{m^3}{min}\). How fast is the height of the water increasing?