Differentiation Rules Cheat Sheet

Power Rule and Derivative of a Constant: A Guide to Differentiation

Understanding the Power Rule

The Power Rule is a fundamental principle in calculus that helps us find the derivative of a power function. When we differentiate a power function of the form f(x) = x^a, where a is a real number, the Power Rule states that:

f'(x) = a * x^(a-1)

For example, the derivative of f(x) = x^3 is f'(x) = 3x^2.

Derivative of a Constant

Another important concept in differentiation is the derivative of a constant function. When we differentiate a constant function f(x) = a, where a is a constant, the derivative is zero:

f'(x) = 0

This means that the graph of a constant function is a horizontal line with zero slope.

Expanding Our Toolkit

In the upcoming chapters, we will delve into more advanced rules and methods for differentiation. These concepts will empower us to differentiate a wide range of functions, including polynomials, rational functions, and trigonometric functions.

Symbolab Derivatives Cheat Sheet

For quick reference, here's a summary of the Power Rule and Derivative of a Constant:

Function	Derivative
f(x) = x^a	f'(x) = a * x^(a-1)
f(x) = a	f'(x) = 0

Conclusion

The Power Rule and Derivative of a Constant are essential building blocks for understanding differentiation. As we progress in our study of calculus, these concepts will continue to serve as foundational principles for solving more complex differentiation problems.