Calculus Examples

Find the Derivative - d/d@VAR f(x) = square root of (1-2x)/(1+2x)
Step 1
Use to rewrite as .
Step 2
Differentiate using the chain rule, which states that is where and .
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Step 2.1
To apply the Chain Rule, set as .
Step 2.2
Differentiate using the Power Rule which states that is where .
Step 2.3
Replace all occurrences of with .
Step 3
To write as a fraction with a common denominator, multiply by .
Step 4
Combine and .
Step 5
Combine the numerators over the common denominator.
Step 6
Simplify the numerator.
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Step 6.1
Multiply by .
Step 6.2
Subtract from .
Step 7
Move the negative in front of the fraction.
Step 8
Differentiate using the Quotient Rule which states that is where and .
Step 9
Differentiate.
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Step 9.1
By the Sum Rule, the derivative of with respect to is .
Step 9.2
Since is constant with respect to , the derivative of with respect to is .
Step 9.3
Add and .
Step 9.4
Since is constant with respect to , the derivative of with respect to is .
Step 9.5
Differentiate using the Power Rule which states that is where .
Step 9.6
Simplify the expression.
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Step 9.6.1
Multiply by .
Step 9.6.2
Move to the left of .
Step 9.7
By the Sum Rule, the derivative of with respect to is .
Step 9.8
Since is constant with respect to , the derivative of with respect to is .
Step 9.9
Add and .
Step 9.10
Since is constant with respect to , the derivative of with respect to is .
Step 9.11
Multiply by .
Step 9.12
Differentiate using the Power Rule which states that is where .
Step 9.13
Simplify terms.
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Step 9.13.1
Multiply by .
Step 9.13.2
Multiply by .
Step 9.13.3
Move to the left of .
Step 9.13.4
Cancel the common factor of and .
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Step 9.13.4.1
Factor out of .
Step 9.13.4.2
Factor out of .
Step 9.13.4.3
Factor out of .
Step 9.13.4.4
Cancel the common factors.
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Step 9.13.4.4.1
Factor out of .
Step 9.13.4.4.2
Cancel the common factor.
Step 9.13.4.4.3
Rewrite the expression.
Step 10
Simplify.
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Step 10.1
Change the sign of the exponent by rewriting the base as its reciprocal.
Step 10.2
Apply the product rule to .
Step 10.3
Apply the distributive property.
Step 10.4
Apply the distributive property.
Step 10.5
Combine terms.
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Step 10.5.1
Multiply by .
Step 10.5.2
Multiply by .
Step 10.5.3
Multiply by .
Step 10.5.4
Multiply by .
Step 10.5.5
Subtract from .
Step 10.5.6
Add and .
Step 10.5.7
Subtract from .
Step 10.5.8
Move the negative in front of the fraction.
Step 10.5.9
Multiply by .
Step 10.5.10
Move to the left of .
Step 10.5.11
Move to the denominator using the negative exponent rule .
Step 10.5.12
Multiply by by adding the exponents.
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Step 10.5.12.1
Move .
Step 10.5.12.2
Use the power rule to combine exponents.
Step 10.5.12.3
To write as a fraction with a common denominator, multiply by .
Step 10.5.12.4
Combine and .
Step 10.5.12.5
Combine the numerators over the common denominator.
Step 10.5.12.6
Simplify the numerator.
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Step 10.5.12.6.1
Multiply by .
Step 10.5.12.6.2
Add and .