Calculus Examples

Find the Derivative - d/dx y=(3tan(x))/(2pi-sin(x))
Step 1
Since is constant with respect to , the derivative of with respect to is .
Step 2
Differentiate using the Quotient Rule which states that is where 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
Combine and .
Step 7
Simplify.
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Step 7.1
Apply the distributive property.
Step 7.2
Apply the distributive property.
Step 7.3
Simplify the numerator.
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Step 7.3.1
Simplify each term.
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Step 7.3.1.1
Rewrite in terms of sines and cosines.
Step 7.3.1.2
Apply the product rule to .
Step 7.3.1.3
One to any power is one.
Step 7.3.1.4
Multiply .
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Step 7.3.1.4.1
Combine and .
Step 7.3.1.4.2
Combine and .
Step 7.3.1.5
Multiply .
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Step 7.3.1.5.1
Combine and .
Step 7.3.1.5.2
Multiply by .
Step 7.3.1.6
Rewrite in terms of sines and cosines.
Step 7.3.1.7
Apply the product rule to .
Step 7.3.1.8
One to any power is one.
Step 7.3.1.9
Combine and .
Step 7.3.1.10
Multiply .
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Step 7.3.1.10.1
Multiply by .
Step 7.3.1.10.2
Combine and .
Step 7.3.1.11
Move the negative in front of the fraction.
Step 7.3.1.12
Rewrite in terms of sines and cosines, then cancel the common factors.
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Step 7.3.1.12.1
Rewrite in terms of sines and cosines.
Step 7.3.1.12.2
Cancel the common factors.
Step 7.3.2
Simplify each term.
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Step 7.3.2.1
Factor out of .
Step 7.3.2.2
Separate fractions.
Step 7.3.2.3
Convert from to .
Step 7.3.2.4
Separate fractions.
Step 7.3.2.5
Convert from to .
Step 7.3.2.6
Divide by .
Step 7.3.2.7
Multiply by .
Step 7.4
Combine terms.
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Step 7.4.1
Multiply by .
Step 7.4.2
Combine.
Step 7.4.3
Apply the distributive property.
Step 7.4.4
Cancel the common factor of .
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Step 7.4.4.1
Cancel the common factor.
Step 7.4.4.2
Rewrite the expression.
Step 7.4.5
Move to the left of .
Step 7.5
Reorder terms.