Calculus Examples

Find the Derivative - d/dx (1+sin(x))/(1-sin(x))
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
Since is constant with respect to , the derivative of with respect to is .
Step 2.3
Add and .
Step 3
The derivative of with respect to is .
Step 4
Differentiate.
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Step 4.1
By the Sum Rule, the derivative of with respect to is .
Step 4.2
Since is constant with respect to , the derivative of with respect to is .
Step 4.3
Add and .
Step 4.4
Since is constant with respect to , the derivative of with respect to is .
Step 4.5
Multiply.
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Step 4.5.1
Multiply by .
Step 4.5.2
Multiply by .
Step 5
The derivative of with respect to is .
Step 6
Simplify.
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Step 6.1
Apply the distributive property.
Step 6.2
Apply the distributive property.
Step 6.3
Simplify the numerator.
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Step 6.3.1
Combine the opposite terms in .
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Step 6.3.1.1
Add and .
Step 6.3.1.2
Add and .
Step 6.3.2
Simplify each term.
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Step 6.3.2.1
Multiply by .
Step 6.3.2.2
Multiply by .
Step 6.3.3
Add and .