Calculus Examples

Find the Derivative - d/d@VAR f(x)=(2x)/(1-x)
Step 1
Since is constant with respect to , the derivative of with respect to is .
Step 2
Differentiate using the Quotient Rule which states that is where and .
Step 3
Differentiate.
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Step 3.1
Differentiate using the Power Rule which states that is where .
Step 3.2
Multiply by .
Step 3.3
By the Sum Rule, the derivative of with respect to is .
Step 3.4
Since is constant with respect to , the derivative of with respect to is .
Step 3.5
Add and .
Step 3.6
Since is constant with respect to , the derivative of with respect to is .
Step 3.7
Multiply.
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Step 3.7.1
Multiply by .
Step 3.7.2
Multiply by .
Step 3.8
Differentiate using the Power Rule which states that is where .
Step 3.9
Simplify terms.
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Step 3.9.1
Multiply by .
Step 3.9.2
Add and .
Step 3.9.3
Add and .
Step 3.9.4
Combine and .
Step 3.9.5
Reorder terms.