1 2 3 4 5 6 7 8 9 10

0:0010 lessons across the whole video52:50

You will be able to

Apply the power rule to differentiate monomials and constant multiples of monomials
Find derivatives of polynomials and evaluate them to get the slope of a tangent line at a given x
Derive the derivative of x² from the limit definition and explain how it relates to secant and tangent slopes
Differentiate rational functions and radical expressions by rewriting them with negative or rational exponents
Use the product rule and quotient rule, and recall the derivatives of sin, cos, tan, sec and cot
Simplify expressions by distributing or dividing before differentiating

Good to know first

Laws of exponents (multiplying, dividing and raising powers)
Slope of a line and the formula (y2 - y1)/(x2 - x1)
Function notation and substituting values into a function
Basic algebra: FOIL, combining like terms and simplifying fractions

Syllabus

10 lessons and a final project

1
Derivatives of constants and what a derivative means Free
0:00–0:371 min of video
The derivative of any constant is zero, because a constant never changes. A derivative is a function that gives the slope of the original function at any x value.
1 formula2 exercises3 questions
2
The Power Rule and Constant Multiples Beyond Pass
0:37–8:007 min of video
You will learn the power rule for differentiating x to a power, and the constant multiple rule for pulling a number out in front. Together they let you differentiate any monomial like 4x^7 in a few seconds.
2 formulas2 exercises4 questions
3
Limit definition and tangent slopes Beyond Pass
8:00–20:0912 min of video
You learn the limit definition of the derivative, f'(x) = lim h→0 [f(x+h) − f(x)]/h, and use it to confirm that the derivative of x² is 2x. You also see that the derivative gives the slope of the tangent line, and that secant slopes with points close together approximate it.
2 code3 exercises
4
Derivatives of polynomials and slopes of tangent lines Beyond Pass
20:09–26:246 min of video
You learn to differentiate polynomials term by term with the power rule, the constant multiple rule and the rule that a constant's derivative is zero. You then use the derivative to find the slope of a tangent line at a given x-value.
3 formulas3 exercises4 questions
5
Negative exponents and reciprocal functions Beyond Pass
26:24–30:444 min of video
You will learn to turn a reciprocal function like 1/x or 8/x^4 into a power with a negative exponent, so the power rule can differentiate it. You will then move the power back into a fraction to write a clean final answer.
2 exercises3 questions
6
Derivatives of radicals using rational exponents Beyond Pass
30:44–36:065 min of video
You learn to turn any radical into a rational exponent, apply the power rule, and turn the answer back into a radical. The method works for square roots, cube roots and higher roots.
3 formulas3 exercises3 questions
7
Simplifying before differentiating Beyond Pass
36:06–41:065 min of video
Some functions are hard to differentiate in their given form, so you first rewrite them as a sum of simple powers of x. Once every term is a plain power like c·x^n, the power rule finds the derivative term by term.
3 code5 build steps3 exercises4 questions
8
Derivatives of trigonometric functions Beyond Pass
41:06–42:472 min of video
You learn the six standard derivatives of the trigonometric functions sine, cosine, secant, cosecant, tangent and cotangent. You also learn a memory trick for the signs, so you can use them in later problems.
9
The Product Rule (including three factors) Beyond Pass
42:47–49:397 min of video
The product rule tells you how to differentiate two functions multiplied together: differentiate one factor, keep the other, add the two results. It extends to three factors by differentiating one factor at a time while the others stay the same.
1 exercise4 questions
10
The Quotient Rule Beyond Pass
49:39–52:503 min of video
The quotient rule tells you how to differentiate a fraction f/g when both the top and bottom are functions of x. You will learn the formula, how to label f and g, and how to simplify the result, using d/dx[(5x+6)/(3x-7)] as the example.
5 build steps2 exercises3 questions

Final project

Tangent Line Lab: A Mini Derivative Calculator

Build a small Python tool that differentiates polynomial-style functions with the power rule, then checks its answers against secant slopes. Use it to find tangent lines and to test the product and quotient rules on real examples. This ties the rules to what a derivative means: the slope of a tangent line.

Its 6 tasks open with Beyond Pass.

Free preview · Lesson 1 in full

Derivatives of constants and what a derivative means

The derivative of any constant is zero, because a constant never changes. A derivative is a function that gives the slope of the original function at any x value.

0:00 to 0:37 in the video

Scratchpad

Draw and write next to the video.

Words to know

Derivative: A function that gives the slope of another function at every x value.
Constant: A fixed number that does not change, such as 5 or -7.
Slope: How steeply a line or curve rises (positive) or falls (negative).
Tangent line: A straight line that just touches a curve at one point and has the same slope as the curve there.

Formulas

\frac{d}{d x} [c] = 0

The derivative of a constant c with respect to x is zero.

$c$: any constant number, such as 5 or -7
$\frac{d}{d x}$: the operation of taking the derivative with respect to x

Worked example

Find $\frac{d}{d x} (5)$ and $\frac{d}{d x} (- 7)$ .

5 is a constant, so its derivative is 0.
-7 is also a constant, so its derivative is 0 too.

Both derivatives are 0.

Practice

Calculate Solution checked

Find $\frac{d}{d x} (12)$ .

Hint

Constants never change.

Solution

12 is a constant.
The derivative of any constant is 0.

Explain Solution checked

In your own words, explain why the derivative of a constant is zero, using the idea of slope.

Hint

Think about what the graph of y = 5 looks like.

Solution

A constant function's graph is a flat horizontal line.
A flat line has slope 0 everywhere, and the derivative gives the slope at each x.
So the derivative of any constant is 0.

A constant's graph is flat, so its slope is 0 at every x; the derivative gives that slope, so it is 0.

On your scratchpad

Draw two axes. Sketch the horizontal line y = 5, then draw a small tangent line at x = 2 and x = 4. Write the slope you see for each tangent.

Quiz

What is the derivative of the constant 5?
1. 0
2. 5
3. 1
4. 5x
Show the answer
A. 0 · A constant never changes, so its derivative is 0.
0:19 watch the moment
What does a derivative give you?
1. The slope of the original function at any x value
2. The area under the curve
3. The y-intercept of the function
4. The original function's maximum value
Show the answer
A. The slope of the original function at any x value · The video says a derivative is a function that gives the slope at some x value.
0:25 watch the moment
What is the derivative of -7?
1. -7
2. 7
3. 1
4. 0
Show the answer
D. 0 · -7 is a constant, so its derivative is 0.
0:19 watch the moment

Open lesson 1, with the video →

Lessons 2–10 and the final project

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Made by Beyond from the video “Calculus 1 - Derivatives” by The Organic Chemistry Tutor. The video plays in YouTube's own player. Watch it on YouTube · All lessons

10 lessons and a final project

Derivatives of constants and what a derivative means Free

The Power Rule and Constant Multiples Beyond Pass

Limit definition and tangent slopes Beyond Pass

Derivatives of polynomials and slopes of tangent lines Beyond Pass

Negative exponents and reciprocal functions Beyond Pass

Derivatives of radicals using rational exponents Beyond Pass

Simplifying before differentiating Beyond Pass

Derivatives of trigonometric functions Beyond Pass

The Product Rule (including three factors) Beyond Pass

The Quotient Rule Beyond Pass