Calculus Examples

Find Where dy/dx is Equal to Zero
Step 1
Differentiate both sides of the equation.
Step 2
The derivative of with respect to is .
Step 3
Differentiate the right side of the equation.
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Differentiate.
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By the Sum Rule, the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Evaluate .
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Since is constant with respect to , the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Multiply by .
Reorder terms.
Step 4
Reform the equation by setting the left side equal to the right side.
Step 5
Replace with .
Step 6
Set then solve for in terms of .
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Subtract from both sides of the equation.
Divide each term in by and simplify.
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Divide each term in by .
Simplify the left side.
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Cancel the common factor of .
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Cancel the common factor.
Divide by .
Simplify the right side.
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Move the negative in front of the fraction.
Step 7
Solve for .
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Remove parentheses.
Remove parentheses.
Simplify .
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Simplify each term.
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Use the power rule to distribute the exponent.
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Apply the product rule to .
Apply the product rule to .
Raise to the power of .
Multiply by .
One to any power is one.
Raise to the power of .
Cancel the common factor of .
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Factor out of .
Cancel the common factor.
Rewrite the expression.
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Multiply by .
Multiply by .
Combine the numerators over the common denominator.
Add and .
Move the negative in front of the fraction.
Step 8
Find the points where .
Step 9
Enter YOUR Problem
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