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Calculus Examples
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
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.
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
Step 7.1
Apply the distributive property.
Step 7.2
Apply the distributive property.
Step 7.3
Simplify the numerator.
Step 7.3.1
Simplify each term.
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 .
Step 7.3.1.4.1
Combine and .
Step 7.3.1.4.2
Combine and .
Step 7.3.1.5
Multiply .
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 .
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.
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.
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.
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 .
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.