Calculus Examples

Find the Derivative - d/dx y=(x^2+b^2)/(x^2-b^2)
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
Move to the left of .
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
Apply the distributive property.
Step 3.3
Apply the distributive property.
Step 3.4
Apply the distributive property.
Step 3.5
Simplify the numerator.
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Step 3.5.1
Combine the opposite terms in .
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Step 3.5.1.1
Subtract from .
Step 3.5.1.2
Add and .
Step 3.5.2
Multiply by .
Step 3.5.3
Subtract from .
Step 3.6
Move the negative in front of the fraction.
Step 3.7
Simplify the denominator.
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Step 3.7.1
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 3.7.2
Apply the product rule to .