All Calculus 1 Resources
Example Questions
Example Question #851 : How To Find Differential Functions
Find the first derivative of the following function:
To find the first derivative of this particular function is accomplished by applying the power rule which states,
Applying the above rule to the equation,
results in,
Example Question #852 : How To Find Differential Functions
Find the first derivative of the function .
To take the derivative, you first use the power rule for differentiating,
,
then you use the chain rule,
.
Also recall the trigonometric rule for differentiating sine,
This produces,
.
Example Question #1031 : Differential Functions
Find the derivative.
Use the quotient rule to find the derivative which states,
.
Given,
the derivatives can be found using the power rule which states,
therefore,
Applying the quotient rule to our function we find the derivative to be as follows.
Simplify.
Example Question #851 : How To Find Differential Functions
Find the derivative.
Use the power rule to find the derivative.
The power rule states,
.
Applying this rule to the function in the problem results in the following.
Example Question #852 : How To Find Differential Functions
Find the derivative.
Use the power rule to find the derivative.
The power rule states,
.
Applying this rule to each term of the function results in the following.
Thus, the derivative is 4.
Example Question #855 : How To Find Differential Functions
What is the equation for the slope of the tangent line to:
To find the equation for the slope of the tangent line, find the derivative.
To find the derivative, use the power rule.
The power rule states,
.
Applying the power rule to each term in the function results in,
.
Thus, the derivative is .
Example Question #856 : How To Find Differential Functions
Find the derivative when .
Use the power rule to find the derivative.
The power rule states,
.
Applying the power rule to each term within the function results in the following.
Thus, the derivative is
Now, substitute for .
Example Question #857 : How To Find Differential Functions
Find the derivative when .
First, use the power rule to find the derivative.
The power rule states,
.
Applying the power rule to each term in the function results in the following.
Thus, the derivative is .
Now, substitute 2 for x.
.
Example Question #858 : How To Find Differential Functions
Find the derivative.
Use the product rule to find the derivative.
The product rule states,
.
Given,
and recalling the trigonometry derivative for cosine is,
the derivatives are as follows.
Therefore, using the product rule the derivative becomes,
.
Example Question #859 : How To Find Differential Functions
Find the derivative.
Use the power rule to find the derivative.
The power rule states,
.
Applying the power rule to each term in the function results in the following.
.
Thus, the derivative is .
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