Calculus Examples

Find the Derivative - d/dx xsin(1/x)
Step 1
Differentiate using the Product Rule which states that is where and .
Step 2
Differentiate using the chain rule, which states that is where and .
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Step 2.1
To apply the Chain Rule, set as .
Step 2.2
The derivative of with respect to is .
Step 2.3
Replace all occurrences of with .
Step 3
Differentiate using the Power Rule.
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Step 3.1
Rewrite as .
Step 3.2
Differentiate using the Power Rule which states that is where .
Step 4
Raise to the power of .
Step 5
Use the power rule to combine exponents.
Step 6
Simplify the expression.
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Step 6.1
Add and .
Step 6.2
Move to the left of .
Step 6.3
Rewrite as .
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
Rewrite the expression using the negative exponent rule .
Step 9.2
Combine and .