Calculus 2 : Calculus II
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Example Questions
Example Question #1491 : Calculus Ii
Compute the first derivative of the following function:
This derivative is calculated with use if the chain rule:
First, we take the derivative of natural log:
Then, we multiply by the derivative of the term inside the natural log:
Finally, this is multiplied by the derivative of the term inside the cosine:
Then, we simplify and make use of the definition of cotangent;
Example Question #361 : Derivative Review
Compute the second derivative of the following function:
To find the second derivative of the function
First, we have to take the second derivative:
Then, we take the derivative of f'(x) to get the second derivative of f(x):
The only derivative rule needed here is the power rule:
Example Question #1493 : Calculus Ii
Compute the first derivative of the following function:
The quotient rule for derivatives is:
Where in our case:
and the derivatives of these functions are:
Applying the quotient rule to these functions, we get:
Factoring out a four from both the numerator and denominator we can simplify this expression to get our final answer:
Example Question #361 : Derivative Review
Compute the first derivative of the following function:
he quotient rule for derivatives is:
Where in our case:
and the derivatives of these functions are:
Applying the quotient rule to our function, we get:
Simplified, we get:
Example Question #1495 : Calculus Ii
Compute the first derivative of the following function:
This problem requires a combination of the quotient and chain rules:
The quotient rule for derivatives is:
Where in our case:
and the derivatives of these functions are:
Applying the quotient rule to these functions, we get:
Simplifying this expression, we get:
Example Question #371 : Derivatives
Compute the first derivative of the following function:
The first term of the function's derivative is found simply with the power rule:
The second term is a trig derivative with the chain rule:
The third term requires the rule for derivatives of exponential and the chain rule:
Combining these three terms, we get the final answer:
Example Question #1493 : Calculus Ii
Compute the first derivative of the following function using the product rule:
The rule for the derivative of the product of two functions is as follows:
For the expression given, the two functions are:
Whose derivatives are:
The derivative of the product is then:
Simplified, this reduces to:
Example Question #173 : First And Second Derivatives Of Functions
Compute the first derivative of the following function:
The rule for the derivative of the product of two functions is as follows:
For the expression given, the two functions are:
Whose derivatives are:
The derivative of the product is then:
Simplifying, we get:
Example Question #1494 : Calculus Ii
Find the first derivative of 
Step 1: Use the power rule on the first term...
Step 2: Take derivative of second term...
Note: The derivative of a(n) constant term is always zero.
The first derivative is
Example Question #175 : First And Second Derivatives Of Functions
What is the first derivative of 
Step 1: Find the derivative of 
Step 2: Plug in the functions into the quotient rule formula:
Step 3: Simplify...
Step 4: Reduce:
The first derivative is
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