Calculus 2 : Calculus II
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Example Questions
Example Question #1471 : Calculus Ii
If 
To find the second derivative, first one has to find the first derivative, then take the derivative of this result.
The derivative of 
The derivative of 
Example Question #1472 : Calculus Ii
What is the second derivative of 
First, you have to take the first derivative. Multiply the exponent by the coefficient in front of the x term and then also subtract one from the exponent:
Now, take the second derivative from the first derivative, using the same process:
Example Question #345 : Derivative Review
What is the derivative of 
Recall that when taking the derivative, multiply the exponent by the coefficient in front of the x term and then subtract one from the exponent:
Simplify to get your answer:
Example Question #142 : First And Second Derivatives Of Functions
What is the first derivative of 
Step 1: Take derivative of
The derivative of 
Step 2: We will use Quotient Rule on the fraction:
First, 
Second, find 
Use the formula:
Step 3: Take the derivatives from step 1 and step 2 and add them up..
The derivative of 
Example Question #346 : Derivative Review
To take the derivative, multiply the exponent by the coefficient in front of the x term and then subtract one from the exponent:
Therefore, your answer is:
Example Question #1476 : Calculus Ii
Find the derivative of
This is a chain rule derivative. For those problems, we need to start with the outermost derivative and work our way inwards. The very outermost function is 
In the last step, we take advantage that
Example Question #351 : Derivatives
Find the derivative of the following function:
First, we need to simplify the problem by distributing through the parenthesis.
Remember, for the second term, if we add exponents when multiplying functions with a common base.
Now, let's take the derivative! The function 
Example Question #351 : Derivative Review
Find the derivative of the following function:
For polynomial derivatives, we use the power rule. We move the exponent to front of the function (and multiply it by the existing coefficient). Then, we reduce each exponent by one.
Example Question #151 : First And Second Derivatives Of Functions
Find the first and second derivatives of the function,
First Derivative
Second Derivative
First Derivative
Second Derivative
First Derivative
Second Derivative
First Derivative
Second Derivative
First Derivative
Second Derivative
First Derivative
Second Derivative
Finding the first derivative:
Recall the derivative of the natural logarithm function is,
Proceed using equation (1) and the chain rule,
To find the second derivative, use the quotient rule on equation (2).
Example Question #351 : Derivative Review
Determine the second derivative of a function 
None
Step 1: Find the first derivative of the function:
By using the power rule which states, 
Step 2: Find the second derivative. To do this, just take the derivative of the former function by using the power rule again.
Remember: The derivative of a constant is always zero!!
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