Calculus Examples

Find the Derivative - d/dx cos(1/x)
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
Differentiate using the Power Rule.
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Step 2.1
Rewrite as .
Step 2.2
Differentiate using the Power Rule which states that is where .
Step 2.3
Multiply.
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Step 2.3.1
Multiply by .
Step 2.3.2
Multiply by .
Step 3
Simplify.
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Step 3.1
Rewrite the expression using the negative exponent rule .
Step 3.2
Combine and .