Calculus Examples

Find Where dy/dx is Equal to Zero
Differentiate both sides of the equation.
The derivative of with respect to is .
Differentiate the right side of the equation.
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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 .
Since is constant with respect to , the derivative of with respect to is .
Add and .
Reform the equation by setting the left side equal to the right side.
Replace with .
Set then solve for in terms of .
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Rewrite the equation as .
Subtract from both sides of the equation.
Divide each term by and simplify.
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Divide each term in by .
Reduce the expression by cancelling the common factors.
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Cancel the common factor.
Divide by .
Solve for .
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Simplify each term.
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Apply the product rule to .
Raise to the power of .
Multiply by .
Apply the product rule to .
Raise to the power of .
Raise to the power of .
Simplify .
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Multiply by .
Write as a fraction with denominator .
Multiply and .
Multiply by .
Move the negative in front of the fraction.
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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Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
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Multiply by .
Multiply by .
Subtract from .
Move the negative in front of the fraction.
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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Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
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Multiply by .
Multiply by .
Subtract from .
Move the negative in front of the fraction.
Find the points where .
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