Enter a problem...
Calculus Examples
Step 1
Differentiate using the Product Rule which states that is where and .
Step 2
The derivative of with respect to is .
Step 3
Step 3.1
To apply the Chain Rule, set as .
Step 3.2
The derivative of with respect to is .
Step 3.3
Replace all occurrences of with .
Step 4
Step 4.1
Since is constant with respect to , the derivative of with respect to is .
Step 4.2
Differentiate using the Power Rule which states that is where .
Step 4.3
Simplify the expression.
Step 4.3.1
Multiply by .
Step 4.3.2
Move to the left of .
Step 5
Step 5.1
Reorder terms.
Step 5.2
Simplify each term.
Step 5.2.1
Rewrite in terms of sines and cosines.
Step 5.2.2
Combine and .
Step 5.2.3
Apply the sine double-angle identity.
Step 5.2.4
Cancel the common factor of .
Step 5.2.4.1
Cancel the common factor.
Step 5.2.4.2
Divide by .
Step 5.2.5
Rewrite in terms of sines and cosines.
Step 5.2.6
Multiply .
Step 5.2.6.1
Combine and .
Step 5.2.6.2
Combine and .
Step 5.2.6.3
Raise to the power of .
Step 5.2.6.4
Raise to the power of .
Step 5.2.6.5
Use the power rule to combine exponents.
Step 5.2.6.6
Add and .
Step 5.2.7
Rewrite in terms of sines and cosines.
Step 5.2.8
Multiply .
Step 5.2.8.1
Combine and .
Step 5.2.8.2
Combine and .
Step 5.3
Simplify each term.
Step 5.3.1
Factor out of .
Step 5.3.2
Separate fractions.
Step 5.3.3
Convert from to .
Step 5.3.4
Divide by .
Step 5.3.5
Separate fractions.
Step 5.3.6
Rewrite as a product.
Step 5.3.7
Write as a fraction with denominator .
Step 5.3.8
Simplify.
Step 5.3.8.1
Divide by .
Step 5.3.8.2
Convert from to .
Step 5.3.9
Divide by .