Calculus Examples

Find the Derivative - d/dx sec(1/2x)tan(1/2x)
Step 1
Combine fractions.
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Step 1.1
Combine and .
Step 1.2
Combine and .
Step 2
Differentiate using the Product Rule which states that is where and .
Step 3
Differentiate using the chain rule, which states that is where and .
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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
Raise to the power of .
Step 5
Use the power rule to combine exponents.
Step 6
Differentiate.
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Step 6.1
Add and .
Step 6.2
Since is constant with respect to , the derivative of with respect to is .
Step 6.3
Combine and .
Step 6.4
Differentiate using the Power Rule which states that is where .
Step 6.5
Multiply by .
Step 7
Differentiate using the chain rule, which states that is where and .
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Step 7.1
To apply the Chain Rule, set as .
Step 7.2
The derivative of with respect to is .
Step 7.3
Replace all occurrences of with .
Step 8
Raise to the power of .
Step 9
Raise to the power of .
Step 10
Use the power rule to combine exponents.
Step 11
Add and .
Step 12
Since is constant with respect to , the derivative of with respect to is .
Step 13
Combine fractions.
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Step 13.1
Combine and .
Step 13.2
Combine and .
Step 14
Differentiate using the Power Rule which states that is where .
Step 15
Multiply by .