All Calculus 2 Resources
Example Questions
Example Question #46 : Derivatives
Find dy/dx:
Before attempting to take the derivative of the given function, the following identity must be realized:
Using this identity, the given function can be simplified to:
From this taking the derivative is a fairly straightforward process:
We can simplify this expression by placing all the terms under a common denominator like so:
This is one of the answer choices.
Example Question #41 : Derivative Review
Use a definition of the derivative with the function to evaluate the following limit:
Using the definition
And plugging in our function, we get that
.
if we factor out inside the limit we get
since the term doesn't contain an h we can factor it out, and then divide by both sides, getting that
but we know that
So we find that the limit is equal to .
Example Question #1171 : Calculus Ii
If the definition of the derivative is used to find the derivative of . Which of these expressions must be evaluated?
None of the other answers
The definition of the derivative of a function is given by
With , we substitute
into our function, and get
. Substituting these into the formula gives us
.
Note: this limit is not easy to evaluate by hand, it would be easier to find the derivative using the Product Rule.
Example Question #41 : Derivative Review
Example Question #41 : Definition Of Derivative
Find the derivative of using the definition of the derivative.
The definition of a derivative is
Substituting these expressions into the definition of a derivative gives us
Example Question #51 : Definition Of Derivative
Find the derivative of using the definition of the derivative.
The definition of a derivative is
Substituting these expressions into the definition of a derivative gives us
Substituting in the trigonometric identity
Then using the identities
and
Example Question #52 : Derivative Review
Find the derivative of using the definition of the derivative.
The definition of a derivative is
Substituting these expressions into the definition of a derivative gives us
Substituting in the trigonometric identity
Then using the identities
and
Example Question #53 : Derivative Review
Find the derivative of using the definition of the derivative.
The definition of a derivative is
Substituting these expressions into the definition of a derivative gives us
Example Question #54 : Derivative Review
Find the derivative of using the definition of the derivative.
The definition of a derivative is
Substituting these expressions into the definition of a derivative gives us
Example Question #51 : Definition Of Derivative
Find the derivative of using the definition of the derivative.
The definition of a derivative is
Substituting these expressions into the definition of a derivative gives us
All Calculus 2 Resources
