All Calculus AB Resources
Example Questions
Example Question #1 : Use Derivatives Of Natural Logs And Advanced Trig Functions
Which of the following is the derivative of ?
When finding the derivative of we use the power rule by multiplying the coefficient of by the coefficient of . The form of this looks like . This is actually a case of using the Chain Rule, but that will be covered in later topics. So in this case the coefficient of is and the coefficient of is also . So the .
If we were to find the derivative of , then .
Example Question #1 : Use Derivatives Of Natural Logs And Advanced Trig Functions
Find the derivative of the function
We use our rule for finding the derivative of . We know that . In this case, and .
Example Question #2 : Use Derivatives Of Natural Logs And Advanced Trig Functions
Which of the following is the correct derivative for ?
When we are finding the derivative of we are finding the rate of change at a certain point/angle of the function . If we think about finding the derivative using the graph of , we are finding the tangent to at a certain point/angle. Thinking about it this way we can see that the derivative of is given by the of the given angle. The general form for this is
Example Question #3 : Use Derivatives Of Natural Logs And Advanced Trig Functions
Find the derivative of the function .
We will need to use our rule for finding the derivative of , .
Example Question #1 : Use Derivatives Of Natural Logs And Advanced Trig Functions
Which of the following is the correct derivative for ?
To find the derivative of , we use the rule where are constants. We use because is the tangent to the graph of at each given point giving us the rate of change at each given angle of the function .
Example Question #5 : Use Derivatives Of Natural Logs And Advanced Trig Functions
Find the derivative of the function .
We first find the derivative of the quantity of the cosine function. The derivative of is . Now the derivative of is . The quantity of the cosine function will stay the same. So now we use the form to write our derivative.
Example Question #21 : Basic Differentiation Rules
Which of the following is the correct derivative of ?
The rule for finding the derivative of the natural logarithm is if then . So if we wanted to find the derivative of we would have .
Example Question #1 : Use Derivatives Of Natural Logs And Advanced Trig Functions
Find the derivative of the function .
We know that the derivative of is and we also know that when we have to find the derivative of we keep the exponent the same but multiply the coefficient of by the coefficient of .
Example Question #1 : Use Derivatives Of Natural Logs And Advanced Trig Functions
Evaluate
We are able to recognize that this is the definition of derivatives. Once we identify that this is the definition of derivatives we can see that . So this question is really just asking us to find . So our answer here is .
Example Question #1 : Use Derivatives Of Natural Logs And Advanced Trig Functions
Which of the following is the derivative of ?
When finding the derivative of we use the power rule by multiplying the coefficient of by the coefficient of . The form of this looks like . This is actually a case of using the Chain Rule, but that will be covered in later topics. So in this case the coefficient of is and the coefficient of is also . So the .
If we were to find the derivative of , then .