Calculus Examples

Find the Derivative - d/dx arccsc(x/2)
Step 1
Differentiate using the chain rule, which states that is where and .
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Step 1.1
To apply the Chain Rule, set as .
Step 1.2
The derivative of with respect to is .
Step 1.3
Replace all occurrences of with .
Step 2
Combine and .
Step 3
Multiply by the reciprocal of the fraction to divide by .
Step 4
Multiply by .
Step 5
Since is constant with respect to , the derivative of with respect to is .
Step 6
Simplify terms.
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Step 6.1
Multiply by .
Step 6.2
Cancel the common factor of .
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Step 6.2.1
Cancel the common factor.
Step 6.2.2
Rewrite the expression.
Step 7
Differentiate using the Power Rule which states that is where .
Step 8
Multiply by .
Step 9
Simplify.
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Step 9.1
Apply the product rule to .
Step 9.2
Raise to the power of .