30 Calculus Tutorials

These Calculus tutorials are written by experienced educators, all of whom also offer private tutoring lessons. Get the Calculus help you need, whether through these tutorials or through private tutoring lessons.

Differential Equations

Handling of Materials Suppose that we have a tank containing water. Suppose also that we have 2 pumps — one pump can drain the tank in 6 hours, and the other can drain the tank in 5 hours. How long will it take to drain the tank with both pumps running? Since one pump can…

Derivatives and Integrals

Fine a derivative and an integral that are the same.

Different Differentiation Rules

Any problem that can be solved with the quotient rule can also be solved with the product rule and chain rule.

Product Rule Differentiation (Single Variable)

The product rule is used when you are finding the derivative of a function that has one dependent variable expression multiplied by another dependent variable expression. Compare this function: f(x) = x2 + 2×5 …with this function: g(x) = x4cos(x) Function g(x) can be thought of as two separate functions multiplied together: h(x) = x4…

finding domain of a complex function

If in a problem you are required to find the domain of a function which is the sum of two or more functions then the domain of the combined function will be the union of domains of individual function.

Quotient Rule (Single Variable)

The quotient rule is when a larger function is composed of two differentiable functions divided by one another like so:

Basic Derivatives and the Limit Definition

Calculus is said to be the mathematics of derivation, so to understand Calculus, we must first understand derivatives. So, what is a derivative? A derivative is a function that equals the rate of change (slope) at any point of any base function (a function used to find f(x)), even curved functions, in the form of…

The Chain Rule (Simple)

Here, I will be talking about how to find the derivative of a function using The Chain Rule. To start off, I’ll remind you, or tell you, what the derivative is. The derivative of a function is the rate of change of that function at the given point. This is also known as the slope…

Basic derivatives (The power rule)

Differentiating can be a pretty daunting task. Although there are many different rules to follow for more advanced problems, the power rule is the basic rule of derivatives. The derivative of a function provides the equation of the slope of the original function. Each point on the derivative graph gives the instantaneous rate of change…

The Chain Rule

How do we differentiate F(x)=Tan(2x-4)? This function is the composite FoG of two functions F (u)=Tan u and u=2x-4 that we know how to differentiate. The Chain rule states that the correct answer to F(x) is derived by multiplying the derivatives of F and G.