Calculus Examples

Find the Derivative - d/dx y=e^(-(x^2)/2)
Step 1
Differentiate using the chain rule, which states that is where and .
Tap for more steps...
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.
Tap for more steps...
Step 2.1
Since is constant with respect to , the derivative of with respect to is .
Step 2.2
Combine and .
Step 2.3
Differentiate using the Power Rule which states that is where .
Step 2.4
Simplify terms.
Tap for more steps...
Step 2.4.1
Multiply by .
Step 2.4.2
Combine and .
Step 2.4.3
Combine and .
Step 2.4.4
Cancel the common factor of and .
Tap for more steps...
Step 2.4.4.1
Factor out of .
Step 2.4.4.2
Cancel the common factors.
Tap for more steps...
Step 2.4.4.2.1
Factor out of .
Step 2.4.4.2.2
Cancel the common factor.
Step 2.4.4.2.3
Rewrite the expression.
Step 2.4.4.2.4
Divide by .
Step 2.4.5
Reorder factors in .