Precalculus : Introductory Calculus
Study concepts, example questions & explanations for Precalculus
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Example Questions
Example Question #131 : Introductory 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 #755 : Pre 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 #133 : Introductory Calculus
Find the first derivative of the following equation:
To solve, simply use the power rule as outline below:
Power rule:
Thus,
Example Question #757 : Pre 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,
Example Question #1 : Find The Critical Numbers Of A Function
Find the critical value(s) of the function.
To find the critical values of a function, we must set the derivate equal to 0.
First, we find the derivative of the function to be
We can then factor out a 6x and set the expression equal to 0
From here, we can easily determine that
and
Therefore, the critical values of the function are at 
Example Question #3 : Find The Critical Numbers Of A Function
Find the critical points of the following function:
The critical points of a function are the points at which its slope is zero, so first we must take the derivative of the function so we have a function that describes its slope:
Now that we have the derivative, which tells us the slope of f(x) at any point x, we can set it equal to 0 and solve for x to find the points at which the slope of the function is 0, which are our critical points:
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