All AP Calculus BC Resources
Example Questions
Example Question #31 : First And Second Derivatives Of Functions
If , find in terms of and .
None of the other answers
Using a combination of logarithms, implicit differentiation, and a bit of algebra, we have
. Quotient Rule + implicit differentiation.
Example Question #32 : First And Second Derivatives Of Functions
Find the derivative of the function
None of the other answers
None of the other answers
The correct answer is .
Using the Quotient Rule and the fact , we have
.
Example Question #11 : Derivative Rules For Sums, Products, And Quotients
First, factor out : . Now we can differentiate using the product rule, .
Here, so . so .
The answer is
Example Question #12 : Derivative Rules For Sums, Products, And Quotients
According to the product rule, . Here so . so .
The derivative is
Factoring out the 2 gives . Remembering the double angle trigonometric identity finally gives
Example Question #403 : Ap Calculus Bc
If , find
First, we need to find . We can do that by using the quotient rule.
.
Plugging in for and simplifying, we get
.
Example Question #404 : Ap Calculus Bc
Find the derivative of f:
The derivative of the function is equal to
and was found using the following rules:
, , ,
Example Question #405 : Ap Calculus Bc
Find the derivative of the function:
where is a constant
When taking the derivative of the sum, we simply take the derivative of each component.
The derivative of the function is
and was found using the following rules:
,
Example Question #406 : Ap Calculus Bc
Compute the first derivative of the following function.
Compute the first derivative of the following function.
To solve this problem, we need to apply the product rule:
So, we need to apply this rule to each of the terms in our function. Let's start with the first term
Next, let's tackle the second part
Now, combine the two to get:
Example Question #407 : Ap Calculus Bc
Evaluate the derivative of the function .
Use the product rule:
where and .
By the power rule, .
By the chain rule, .
Therefore, the derivative of the entire function is:
.
Example Question #408 : Ap Calculus Bc
Find the second derivative of g(x)
Find the second derivative of g(x)
To find this derivative, we need to use the product rule:
So, let's begin:
So, we are closer, but we need to derive again to get the 2nd derivative
So, our answer is:
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