Calculus Examples

Find the Derivative Using Quotient Rule - d/dx (ax+b)/(cx+d)
Step 1
Differentiate using the Quotient Rule which states that is where and .
Step 2
By the Sum Rule, the derivative of with respect to is .
Step 3
Evaluate .
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Step 3.1
Since is constant with respect to , the derivative of with respect to is .
Step 3.2
Differentiate using the Power Rule which states that is where .
Step 3.3
Multiply by .
Step 4
Differentiate.
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Step 4.1
Since is constant with respect to , the derivative of with respect to is .
Step 4.2
Add and .
Step 4.3
By the Sum Rule, the derivative of with respect to is .
Step 5
Evaluate .
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Step 5.1
Since is constant with respect to , the derivative of with respect to is .
Step 5.2
Differentiate using the Power Rule which states that is where .
Step 5.3
Multiply by .
Step 6
Differentiate using the Constant Rule.
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Step 6.1
Since is constant with respect to , the derivative of with respect to is .
Step 6.2
Add and .
Step 7
Simplify.
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Step 7.1
Apply the distributive property.
Step 7.2
Apply the distributive property.
Step 7.3
Apply the distributive property.
Step 7.4
Combine the opposite terms in .
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Step 7.4.1
Reorder the factors in the terms and .
Step 7.4.2
Subtract from .
Step 7.4.3
Add and .
Step 7.5
Reorder terms.