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Calculus Examples
Step 1
By the Sum Rule, the derivative of with respect to is .
Step 2
Step 2.1
Differentiate using the Product Rule which states that is where and .
Step 2.2
Differentiate using the chain rule, which states that is where and .
Step 2.2.1
To apply the Chain Rule, set as .
Step 2.2.2
Differentiate using the Power Rule which states that is where .
Step 2.2.3
Replace all occurrences of with .
Step 2.3
The derivative of with respect to is .
Step 2.4
Differentiate using the Power Rule which states that is where .
Step 3
Step 3.1
Differentiate using the Product Rule which states that is where and .
Step 3.2
Differentiate using the chain rule, which states that is where and .
Step 3.2.1
To apply the Chain Rule, set as .
Step 3.2.2
Differentiate using the Power Rule which states that is where .
Step 3.2.3
Replace all occurrences of with .
Step 3.3
The derivative of with respect to is .
Step 3.4
Differentiate using the Power Rule which states that is where .
Step 3.5
Multiply by .
Step 3.6
Multiply by .
Step 4
Step 4.1
Rewrite the expression using the negative exponent rule .
Step 4.2
Rewrite the expression using the negative exponent rule .
Step 4.3
Combine terms.
Step 4.3.1
Convert from to .
Step 4.3.2
Convert from to .
Step 4.4
Reorder terms.
Step 4.5
Simplify each term.
Step 4.5.1
Rewrite in terms of sines and cosines.
Step 4.5.2
Apply the product rule to .
Step 4.5.3
One to any power is one.
Step 4.5.4
Multiply .
Step 4.5.4.1
Combine and .
Step 4.5.4.2
Combine and .
Step 4.5.5
Move to the left of .
Step 4.5.6
Combine and .
Step 4.5.7
Rewrite in terms of sines and cosines.
Step 4.5.8
Apply the product rule to .
Step 4.5.9
One to any power is one.
Step 4.6
Simplify each term.
Step 4.6.1
Factor out of .
Step 4.6.2
Separate fractions.
Step 4.6.3
Convert from to .
Step 4.6.4
Combine and .
Step 4.6.5
Factor out of .
Step 4.6.6
Separate fractions.
Step 4.6.7
Rewrite in terms of sines and cosines.
Step 4.6.8
Rewrite as a product.
Step 4.6.9
Simplify.
Step 4.6.9.1
Convert from to .
Step 4.6.9.2
Convert from to .
Step 4.6.10
Multiply .
Step 4.6.10.1
Combine and .
Step 4.6.10.2
Combine and .
Step 4.6.11
Separate fractions.
Step 4.6.12
Rewrite in terms of sines and cosines.
Step 4.6.13
Rewrite as a product.
Step 4.6.14
Simplify.
Step 4.6.14.1
Convert from to .
Step 4.6.14.2
Convert from to .
Step 4.6.15
Divide by .
Step 4.6.16
Multiply .
Step 4.6.16.1
Raise to the power of .
Step 4.6.16.2
Raise to the power of .
Step 4.6.16.3
Use the power rule to combine exponents.
Step 4.6.16.4
Add and .
Step 4.6.17
Rewrite as .
Step 4.6.18
Rewrite as .
Step 4.6.19
Convert from to .