Calculus Examples

Find the Derivative - d/dx (5x^2-9x+13)/(2x+4)
Step 1
Differentiate using the Quotient Rule which states that is where and .
Step 2
Differentiate.
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Step 2.1
By the Sum Rule, the derivative of with respect to is .
Step 2.2
Since is constant with respect to , the derivative of with respect to is .
Step 2.3
Differentiate using the Power Rule which states that is where .
Step 2.4
Multiply by .
Step 2.5
Since is constant with respect to , the derivative of with respect to is .
Step 2.6
Differentiate using the Power Rule which states that is where .
Step 2.7
Multiply by .
Step 2.8
Since is constant with respect to , the derivative of with respect to is .
Step 2.9
Add and .
Step 2.10
By the Sum Rule, the derivative of with respect to is .
Step 2.11
Since is constant with respect to , the derivative of with respect to is .
Step 2.12
Differentiate using the Power Rule which states that is where .
Step 2.13
Multiply by .
Step 2.14
Since is constant with respect to , the derivative of with respect to is .
Step 2.15
Simplify the expression.
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Step 2.15.1
Add and .
Step 2.15.2
Multiply by .
Step 3
Simplify.
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Step 3.1
Apply the distributive property.
Step 3.2
Simplify the numerator.
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Step 3.2.1
Simplify each term.
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Step 3.2.1.1
Expand using the FOIL Method.
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Step 3.2.1.1.1
Apply the distributive property.
Step 3.2.1.1.2
Apply the distributive property.
Step 3.2.1.1.3
Apply the distributive property.
Step 3.2.1.2
Simplify and combine like terms.
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Step 3.2.1.2.1
Simplify each term.
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Step 3.2.1.2.1.1
Rewrite using the commutative property of multiplication.
Step 3.2.1.2.1.2
Multiply by by adding the exponents.
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Step 3.2.1.2.1.2.1
Move .
Step 3.2.1.2.1.2.2
Multiply by .
Step 3.2.1.2.1.3
Multiply by .
Step 3.2.1.2.1.4
Multiply by .
Step 3.2.1.2.1.5
Multiply by .
Step 3.2.1.2.1.6
Multiply by .
Step 3.2.1.2.2
Add and .
Step 3.2.1.3
Multiply by .
Step 3.2.1.4
Multiply by .
Step 3.2.1.5
Multiply by .
Step 3.2.2
Subtract from .
Step 3.2.3
Add and .
Step 3.2.4
Subtract from .
Step 3.3
Factor out of .
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Step 3.3.1
Factor out of .
Step 3.3.2
Factor out of .
Step 3.3.3
Factor out of .
Step 3.3.4
Factor out of .
Step 3.3.5
Factor out of .
Step 3.4
Simplify the denominator.
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Step 3.4.1
Factor out of .
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Step 3.4.1.1
Factor out of .
Step 3.4.1.2
Factor out of .
Step 3.4.1.3
Factor out of .
Step 3.4.2
Apply the product rule to .
Step 3.4.3
Raise to the power of .
Step 3.5
Cancel the common factors.
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Step 3.5.1
Factor out of .
Step 3.5.2
Cancel the common factor.
Step 3.5.3
Rewrite the expression.