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Example Questions
Example Question #141 : First And Second Derivatives Of Functions
What is the first derivative of the following equation?
To solve this problem, we have to use several tricks. First, we take the natural log of each side, so we can bring down the exponent on the right side of the equation, which looks like this:
. Now, we differentiate each side of the equation, keeping in mind that we need to use implicit differentiation for the left side:
. To differentiate the right side, we use a combination of the chain and product rules, which looks like this:
, which becomes:
. This simplifies further to: . Lastly, we multiple both sides of the equation by . This gives us:
. Looking back at our original equation gives our value for . Plugging in this value, we get our answer of:
Example Question #141 : First And Second Derivatives Of Functions
What is the second derivative of ?
Before you can take the second derivative, find the first derivative. Remember to multiply the exponent by the coefficient in front of the x term and then subtract one from the exponent:
Now, take the second derivative from the first derivative:
Example Question #341 : Derivative Review
Find the derivative of .
Remember that when taking the derivative, multiply the exponent by the coefficient in front of the x term and then subtract one from the exponent:
Example Question #1462 : Calculus Ii
What is the second derivative of ?
To take the derivative, multiply the exponent by the coefficient in front of the x term and then also subtract one from the exponent. Take the first derivative:
Now, take the second derivative from the first derivative:
Example Question #344 : Derivative Review
If , what is ?
To find the second derivative, first one has to find the first derivative, then take the derivative of this result.
The derivative of is .
The derivative of is , and this is our final answer.
Example Question #342 : Derivative Review
If , what is ?
To find the second derivative, first one has to find the first derivative, then take the derivative of this result.
The derivative of is .
The derivative of is , and this is our final answer.
Example Question #1472 : Calculus Ii
What is the second derivative of ?
First, you have to take the first derivative. Multiply the exponent by the coefficient in front of the x term and then also subtract one from the exponent:
Now, take the second derivative from the first derivative, using the same process:
Example Question #1473 : Calculus Ii
What is the derivative of ?
Recall that when taking the derivative, multiply the exponent by the coefficient in front of the x term and then subtract one from the exponent:
Simplify to get your answer:
Example Question #1474 : Calculus Ii
What is the first derivative of ?
Step 1: Take derivative of
The derivative of is using the power rule which states .
Step 2: We will use Quotient Rule on the fraction:
First, and :
Second, find and :
Use the formula:
Step 3: Take the derivatives from step 1 and step 2 and add them up..
The derivative of is
.
Example Question #1475 : Calculus Ii
What is the derivative of ?
To take the derivative, multiply the exponent by the coefficient in front of the x term and then subtract one from the exponent:
Therefore, your answer is: