The following diagram gives the basic derivative rules that you may find useful: Constant Rule, Constant Multiple Rule, Power Rule, Sum Rule, Difference Rule, Product Rule, Quotient Rule, and Chain Rule. Scroll down the page for more examples and solutions.
For any real number n,
the derivative of f(x) = xn is f ’(x) = nxn-1
which can also be written as
Using the power rule formula, we find that the derivative of the function f(x) = x would be one.
The derivative of f(x) = x is f ’(x) = 1
which can also be written as
Example:
Differentiate f(x) = x
Solution:
f ’(x) = f ’(x1) = 1x0 = 1Using the power rule formula, we find that the derivative of a function that is a constant would be zero.
For any constant c,
The derivative of f(x) = c is f ’(x) = 0
which can also be written as
Example:
Differentiate the following:
a) f(3)
b) f(157)
Solution:
a) f ‘(3) = f ‘(3x0) = 0(3x-1) = 0The constant multiple rule says that the derivative of a constant value times a function is the constant times the derivative of the function.
If c is a constant and f is a differentiable function, then
Example:
Differentiate the following:
a) y = 2x4
b) y = –x
Solution:
The Sum Rule tells us that the derivative of a sum of functions is the sum of the derivatives.
If f and g are both differentiable, then
The Sum Rule can be extended to the sum of any number of functions.
For example (f + g + h)’ = f’ + g’ + h’
Example:
Differentiate 5x2 + 4x + 7
Solution:
The Difference Rule tells us that the derivative of a difference of functions is the difference of the derivatives.
If f and g are both differentiable, then
Example:
Differentiate x8 – 5x2 + 6x
Solution:
Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.