23 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.

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.

Minimal Volume of a Cone Circumscribed about a Sphere

Find the minimal volume and dimensions of a right circular cone circumscribed about a sphere of a given volume. To solve this problem we need to know 1) The formula for the volume of a sphere V = \frac{4 {\pi} r^{2}}{3} 2) The formula for the volume of a cone $V = \frac{{\pi} r^{2} h}…

Using Derivatives to Find the Slope at a Certain Point

Say you have an equation that asks you to find the slope of a graph at the point x. How would you do this? Using Calculus, you would do this using derivatives. By taking the derivative of the given equation, you can plug in the point at which they want the slope and solve. Finding…

Power rule from limit definition (positive integer exponents)

We will attempt to derive the power rule for derivatives from the limit definition of the derivative. For the purposes of this problem we will limit ourselves to positive integer exponents.


Differentiation of a function y = f(x)^g(x)

The power rule

The power rule is used to take derivatives of a variable raised to a power. When asked to take the derivative of say, x^2 (x squared), you bring the exponent down and multiply it by the existing coefficient, to become a coefficient of the variable, now you look back up at the exponent and subtract…

Integration by Parts

Integration by parts is an important and powerful integration technique that captures the idea of using the product rule of differentiation backwards. Let’s recall the product rule of differentiation: Now suppose we were trying to integrate an expression that could be written as g(x)*f'(x). We tried power rule, u-substitution, and scored our table of integrals,…

Algebraic Evaluation of Limits

We are going to use a simple example to explain key concepts in limit.