Calculus Examples

Find the Derivative - d/dx e^(-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
Differentiate using the Exponential Rule which states that is where =.
Step 1.3
Replace all occurrences of with .
Step 2
Differentiate using the Product Rule which states that is where and .
Step 3
Differentiate.
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Step 3.1
Rewrite as .
Step 3.2
Differentiate using the Power Rule which states that is where .
Step 3.3
Multiply.
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Step 3.3.1
Multiply by .
Step 3.3.2
Multiply by .
Step 3.4
Since is constant with respect to , the derivative of with respect to is .
Step 3.5
Simplify the expression.
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Step 3.5.1
Multiply by .
Step 3.5.2
Add and .
Step 4
Simplify.
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Step 4.1
Rewrite the expression using the negative exponent rule .
Step 4.2
Combine and .