Calculus Examples

Find the Derivative Using Quotient Rule - d/dx
Differentiate using the Quotient Rule which states that is where and .
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 .
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 .
By the Sum Rule, the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Since is constant with respect to , the derivative of with respect to is .
Simplify the expression.
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Add and .
Multiply by .
Simplify.
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Apply the distributive property.
Simplify the numerator.
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Simplify each term.
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Expand using the FOIL Method.
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Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify each term.
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Rewrite using the commutative property of multiplication.
Multiply by by adding the exponents.
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Move .
Multiply by .
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Raise to the power of .
Use the power rule to combine exponents.
Add and .
Move to the left of .
Multiply by .
Multiply by .
Multiply by .
Subtract from .
Add and .
Add and .
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