Calculus Examples

Find the Derivative - d/dx (x+y)/(x-y)
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
Differentiate using the Power Rule which states that is where .
Step 2.3
Since is constant with respect to , the derivative of with respect to is .
Step 2.4
Simplify the expression.
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Step 2.4.1
Add and .
Step 2.4.2
Multiply by .
Step 2.5
By the Sum Rule, the derivative of with respect to is .
Step 2.6
Differentiate using the Power Rule which states that is where .
Step 2.7
Since is constant with respect to , the derivative of with respect to is .
Step 2.8
Simplify the expression.
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Step 2.8.1
Add and .
Step 2.8.2
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
Combine the opposite terms in .
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Step 3.2.1.1
Subtract from .
Step 3.2.1.2
Add and .
Step 3.2.2
Subtract from .
Step 3.3
Move the negative in front of the fraction.