71 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

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

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.

L’Hospital Rule

Is indeterminate form the only condition we need to check before using L’Hospital Rule?

What are Derivatives? Basics of Derivatives.

Derivatives are something heavily used in Calculus. They are used to find the slope of the tangent line of a specific function. There are many different rules for deriving a function but I’m just going to go over a few of them. In this tutorial I’ll cover the basics. First and foremost are constants. If…

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