Calculus Examples

Find dy/dx y=(x^2)/(1-x)
Step 1
Differentiate both sides of the equation.
Step 2
The derivative of with respect to is .
Step 3
Differentiate the right side of the equation.
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Step 3.1
Differentiate using the Quotient Rule which states that is where and .
Step 3.2
Differentiate.
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Step 3.2.1
Differentiate using the Power Rule which states that is where .
Step 3.2.2
Move to the left of .
Step 3.2.3
By the Sum Rule, the derivative of with respect to is .
Step 3.2.4
Since is constant with respect to , the derivative of with respect to is .
Step 3.2.5
Add and .
Step 3.2.6
Since is constant with respect to , the derivative of with respect to is .
Step 3.2.7
Multiply.
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Step 3.2.7.1
Multiply by .
Step 3.2.7.2
Multiply by .
Step 3.2.8
Differentiate using the Power Rule which states that is where .
Step 3.2.9
Multiply by .
Step 3.3
Simplify.
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Step 3.3.1
Apply the distributive property.
Step 3.3.2
Apply the distributive property.
Step 3.3.3
Simplify the numerator.
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Step 3.3.3.1
Simplify each term.
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Step 3.3.3.1.1
Multiply by .
Step 3.3.3.1.2
Multiply by by adding the exponents.
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Step 3.3.3.1.2.1
Move .
Step 3.3.3.1.2.2
Multiply by .
Step 3.3.3.1.3
Multiply by .
Step 3.3.3.2
Add and .
Step 3.3.4
Reorder terms.
Step 3.3.5
Factor out of .
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Step 3.3.5.1
Factor out of .
Step 3.3.5.2
Factor out of .
Step 3.3.5.3
Factor out of .
Step 3.3.6
Factor out of .
Step 3.3.7
Rewrite as .
Step 3.3.8
Factor out of .
Step 3.3.9
Rewrite as .
Step 3.3.10
Move the negative in front of the fraction.
Step 4
Reform the equation by setting the left side equal to the right side.
Step 5
Replace with .