Calculus Examples

Find the Derivative - d/dx (tan(x))/(1+cos(x))
Step 1
Differentiate using the Quotient Rule which states that is where and .
Step 2
The derivative of with respect to is .
Step 3
Differentiate.
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Step 3.1
By the Sum Rule, the derivative of with respect to is .
Step 3.2
Since is constant with respect to , the derivative of with respect to is .
Step 3.3
Add and .
Step 4
The derivative of with respect to is .
Step 5
Multiply.
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Step 5.1
Multiply by .
Step 5.2
Multiply by .
Step 6
Simplify.
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Step 6.1
Apply the distributive property.
Step 6.2
Simplify the numerator.
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Step 6.2.1
Simplify each term.
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Step 6.2.1.1
Multiply by .
Step 6.2.1.2
Rewrite in terms of sines and cosines.
Step 6.2.1.3
Apply the product rule to .
Step 6.2.1.4
One to any power is one.
Step 6.2.1.5
Rewrite in terms of sines and cosines.
Step 6.2.1.6
Apply the product rule to .
Step 6.2.1.7
One to any power is one.
Step 6.2.1.8
Cancel the common factor of .
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Step 6.2.1.8.1
Factor out of .
Step 6.2.1.8.2
Cancel the common factor.
Step 6.2.1.8.3
Rewrite the expression.
Step 6.2.1.9
Rewrite in terms of sines and cosines.
Step 6.2.1.10
Multiply .
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Step 6.2.1.10.1
Combine and .
Step 6.2.1.10.2
Raise to the power of .
Step 6.2.1.10.3
Raise to the power of .
Step 6.2.1.10.4
Use the power rule to combine exponents.
Step 6.2.1.10.5
Add and .
Step 6.2.2
Simplify each term.
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Step 6.2.2.1
Rewrite as .
Step 6.2.2.2
Rewrite as .
Step 6.2.2.3
Convert from to .
Step 6.2.2.4
Convert from to .
Step 6.2.2.5
Factor out of .
Step 6.2.2.6
Separate fractions.
Step 6.2.2.7
Convert from to .
Step 6.2.2.8
Divide by .
Step 6.3
Reorder terms.
Step 6.4
Simplify the numerator.
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Step 6.4.1
Rewrite in terms of sines and cosines.
Step 6.4.2
Multiply .
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Step 6.4.2.1
Combine and .
Step 6.4.2.2
Raise to the power of .
Step 6.4.2.3
Raise to the power of .
Step 6.4.2.4
Use the power rule to combine exponents.
Step 6.4.2.5
Add and .
Step 6.4.3
Rewrite in terms of sines and cosines.
Step 6.4.4
Apply the product rule to .
Step 6.4.5
One to any power is one.
Step 6.4.6
Rewrite in terms of sines and cosines.
Step 6.5
Simplify each term.
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Step 6.5.1
Factor out of .
Step 6.5.2
Separate fractions.
Step 6.5.3
Convert from to .
Step 6.5.4
Divide by .
Step 6.5.5
Rewrite as .
Step 6.5.6
Rewrite as .
Step 6.5.7
Convert from to .
Step 6.5.8
Convert from to .