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Calculus Examples
Step 1
Step 1.1
Find the first derivative.
Step 1.1.1
Differentiate using the Quotient Rule which states that is where and .
Step 1.1.2
Differentiate.
Step 1.1.2.1
Differentiate using the Power Rule which states that is where .
Step 1.1.2.2
Multiply by .
Step 1.1.2.3
By the Sum Rule, the derivative of with respect to is .
Step 1.1.2.4
Differentiate using the Power Rule which states that is where .
Step 1.1.2.5
Since is constant with respect to , the derivative of with respect to is .
Step 1.1.2.6
Simplify by adding terms.
Step 1.1.2.6.1
Add and .
Step 1.1.2.6.2
Multiply by .
Step 1.1.2.6.3
Subtract from .
Step 1.1.2.6.4
Simplify the expression.
Step 1.1.2.6.4.1
Subtract from .
Step 1.1.2.6.4.2
Move the negative in front of the fraction.
Step 1.2
The first derivative of with respect to is .
Step 2
Step 2.1
Set the first derivative equal to .
Step 2.2
Set the numerator equal to zero.
Step 2.3
Since , there are no solutions.
No solution
No solution
Step 3
Step 3.1
Set the denominator in equal to to find where the expression is undefined.
Step 3.2
Solve for .
Step 3.2.1
Set the equal to .
Step 3.2.2
Add to both sides of the equation.
Step 4
Step 4.1
Evaluate at .
Step 4.1.1
Substitute for .
Step 4.1.2
Simplify.
Step 4.1.2.1
Subtract from .
Step 4.1.2.2
The expression contains a division by . The expression is undefined.
Undefined
Undefined
Undefined
Undefined
Step 5
There are no values of in the domain of the original problem where the derivative is or undefined.
No critical points found