Precalculus : Pre-Calculus
Study concepts, example questions & explanations for Precalculus
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Example Questions
Example Question #37 : Find The First Derivative Of A Function
Calculate the derivative of 
The derivative of constants, or numbers, are zero. The term 
The result of 
The answer is 
Example Question #38 : Find The First Derivative Of A Function
Find the derivative of:
To find the derivative of this function, use the power rule and the chain rule.
The power rule is:
The chain rule is to take the derivative of the inner function.
Apply the power rule for the function and the chain rule. The derivative of 
The answer is:
Example Question #751 : Pre Calculus
Find the first derivative of 
To simplify, simply take the derivative according to the rules for derivatives. Thus,
Example Question #132 : Introductory Calculus
Find the first derivative of the following function:
To solve, simply use the power rule and rule for differentiating natural log as outlined below.
Power rule:
Differentiating natural log:
Thus,
Thus, our first derivative is:
Example Question #132 : Introductory Calculus
Find the first derivative of the following function:
To solve, simply differentiate using the power rule for differentiation as outline below.
Thus,
Notice that our constant term disappeared because the derivative of a constant is zero.
Simplifying the above equation, we get:
Thus, our answer is:
Example Question #752 : Pre Calculus
Find the first derivative of the following equation:
To solve, simply use the power rule as outline below:
Power rule:
Thus,
Example Question #134 : Introductory Calculus
Find the first derivative of the following function:
To solve, you must use the product rule as outline below.
Product rule:
Thus,
Distribute the 2x and 2.
Combine like terms to simplify.
Example Question #758 : Pre Calculus
Find the first derivative of the function 
An equivalent form of writing 
Example Question #759 : Pre Calculus
Find the first derivative:
None of the other answers.
Simplify first:
Use the power rule on each term:
Power rule:
Note that constants become zero.
Example Question #1 : Find The Critical Numbers Of A Function
What are the critical 
None of the other answers
A number is critical if it makes the derivative of the expression equal 0.
Therefore, we need to take the derivative of the expression and set it to 0. We can use the power rule for each term of the expression.
Next, we need to factor the expression:
We can now set each term equal to 0 to find the critical numbers:
Therfore, our critical numbers are,
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