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Calculus Examples
Step 1
Differentiate using the Quotient Rule which states that is where and .
Step 2
The derivative of with respect to is .
Step 3
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 3.4
Since is constant with respect to , the derivative of with respect to is .
Step 3.5
Multiply.
Step 3.5.1
Multiply by .
Step 3.5.2
Multiply by .
Step 4
The derivative of with respect to is .
Step 5
Step 5.1
Apply the distributive property.
Step 5.2
Apply the distributive property.
Step 5.3
Simplify the numerator.
Step 5.3.1
Simplify each term.
Step 5.3.1.1
Rewrite in terms of sines and cosines.
Step 5.3.1.2
Combine and .
Step 5.3.1.3
Rewrite in terms of sines and cosines.
Step 5.3.1.4
Multiply .
Step 5.3.1.4.1
Multiply by .
Step 5.3.1.4.2
Raise to the power of .
Step 5.3.1.4.3
Raise to the power of .
Step 5.3.1.4.4
Use the power rule to combine exponents.
Step 5.3.1.4.5
Add and .
Step 5.3.1.5
Rewrite in terms of sines and cosines, then cancel the common factors.
Step 5.3.1.5.1
Add parentheses.
Step 5.3.1.5.2
Reorder and .
Step 5.3.1.5.3
Rewrite in terms of sines and cosines.
Step 5.3.1.5.4
Cancel the common factors.
Step 5.3.1.6
Multiply by .
Step 5.3.1.7
Rewrite in terms of sines and cosines.
Step 5.3.1.8
Rewrite as .
Step 5.3.1.9
Rewrite using the commutative property of multiplication.
Step 5.3.1.10
Rewrite in terms of sines and cosines.
Step 5.3.1.11
Combine and .
Step 5.3.2
Combine the numerators over the common denominator.
Step 5.3.3
Subtract from .
Step 5.3.4
Move the negative in front of the fraction.
Step 5.3.5
Simplify each term.
Step 5.3.5.1
Factor out of .
Step 5.3.5.2
Separate fractions.
Step 5.3.5.3
Convert from to .
Step 5.3.5.4
Separate fractions.
Step 5.3.5.5
Convert from to .
Step 5.3.5.6
Divide by .
Step 5.3.5.7
Separate fractions.
Step 5.3.5.8
Convert from to .
Step 5.3.5.9
Divide by .
Step 5.3.5.10
Multiply by .
Step 5.4
Simplify the numerator.
Step 5.4.1
Factor out of .
Step 5.4.1.1
Factor out of .
Step 5.4.1.2
Factor out of .
Step 5.4.1.3
Factor out of .
Step 5.4.2
Rewrite in terms of sines and cosines.
Step 5.4.3
Rewrite in terms of sines and cosines.
Step 5.4.4
Combine and .
Step 5.5
Factor out of .
Step 5.6
Multiply by .
Step 5.7
Separate fractions.
Step 5.8
Convert from to .
Step 5.9
Convert from to .
Step 5.10
Combine and .
Step 5.11
Reorder factors in .