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Calculus Examples
Step 1
Differentiate both sides of the equation.
Step 2
The derivative of with respect to is .
Step 3
Step 3.1
Differentiate using the Product Rule which states that is where and .
Step 3.2
The derivative of with respect to is .
Step 3.3
Differentiate.
Step 3.3.1
By the Sum Rule, the derivative of with respect to is .
Step 3.3.2
Since is constant with respect to , the derivative of with respect to is .
Step 3.3.3
Add and .
Step 3.4
The derivative of with respect to is .
Step 3.5
Simplify.
Step 3.5.1
Apply the distributive property.
Step 3.5.2
Reorder terms.
Step 3.5.3
Simplify each term.
Step 3.5.3.1
Rewrite in terms of sines and cosines, then cancel the common factors.
Step 3.5.3.1.1
Reorder and .
Step 3.5.3.1.2
Rewrite in terms of sines and cosines.
Step 3.5.3.1.3
Cancel the common factors.
Step 3.5.3.2
Rewrite in terms of sines and cosines.
Step 3.5.3.3
Combine and .
Step 3.5.3.4
Rewrite in terms of sines and cosines.
Step 3.5.3.5
Multiply .
Step 3.5.3.5.1
Multiply by .
Step 3.5.3.5.2
Raise to the power of .
Step 3.5.3.5.3
Raise to the power of .
Step 3.5.3.5.4
Use the power rule to combine exponents.
Step 3.5.3.5.5
Add and .
Step 3.5.3.5.6
Raise to the power of .
Step 3.5.3.5.7
Raise to the power of .
Step 3.5.3.5.8
Use the power rule to combine exponents.
Step 3.5.3.5.9
Add and .
Step 3.5.4
Convert from to .
Step 3.5.5
Rearrange terms.
Step 3.5.6
Apply pythagorean identity.
Step 4
Reform the equation by setting the left side equal to the right side.
Step 5
Replace with .