Calculus 1 : Writing Equations
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Example Questions
Example Question #1292 : Functions
Find the first derivative of the following function.
None of the other answers.
To find the derivative of a function in this form, we must make use of the chain rule, which states that for a give function:
Its derivative is defined as:
In this case we have the function:
which is in the form of the composite function
in which
By similar logic, the derivative of the composite function is
in which
and
As a result, we have that
Example Question #1293 : Functions
Find the first derivative of the following function using the Product Rule.
None of the other answers are correct.
The Product Rule of derivatives states that for a given function:
The derivative is defined as
In this case, for the given function
and the respective derivatives are:
Applying the product rule we get that
Example Question #241 : Equations
Find the first derivative of the given function.
None of the other answers
To find the first derivative of this function, we must make use of the Quotient Rule of derivatives. That is, for a function
The derivative is defined as
In this case
As a result,
Example Question #1295 : Functions
Find the tangent line of the following function containing the point 
The answer is not shown.
First we note that
Now we take the derivative of the function to find the slope of the tangent line.
Using the chain rule we get
Now we want to find the specific slope of the tangent line containing the 
We then find that the slope is
We now plug in these values to slope-intercept form to find the y-intercept of the tangent line.
which gives us
Thus the equation is simply
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