Calculus Examples

Find the Derivative - d/dx xe^(-(x^2)/50)
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
Differentiate using the Exponential Rule which states that is where =.
Step 2.3
Replace all occurrences of with .
Step 3
Differentiate.
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Step 3.1
Since is constant with respect to , the derivative of with respect to is .
Step 3.2
Combine fractions.
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Step 3.2.1
Combine and .
Step 3.2.2
Combine and .
Step 3.3
Differentiate using the Power Rule which states that is where .
Step 3.4
Combine fractions.
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Step 3.4.1
Multiply by .
Step 3.4.2
Combine and .
Step 3.4.3
Combine and .
Step 4
Raise to the power of .
Step 5
Raise to the power of .
Step 6
Use the power rule to combine exponents.
Step 7
Reduce the expression by cancelling the common factors.
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Step 7.1
Add and .
Step 7.2
Cancel the common factor of and .
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Step 7.2.1
Factor out of .
Step 7.2.2
Cancel the common factors.
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Step 7.2.2.1
Factor out of .
Step 7.2.2.2
Cancel the common factor.
Step 7.2.2.3
Rewrite the expression.
Step 7.3
Move the negative in front of the fraction.
Step 8
Differentiate using the Power Rule which states that is where .
Step 9
Multiply by .