Find the Derivative - d/dx e^(-x^2)

Problem

d(e^(−x^2))/d(x)

Solution

1. Identify the outer function and the inner function to apply the Chain Rule. The outer function is e^u and the inner function is u=−x^2

2. Apply the Chain Rule which states that d(e^u)/d(x)=e^u⋅d(u)/d(x)

3. Differentiate the inner function −x^2 with respect to x using the Power Rule.

(d(−)*x^2)/d(x)=−2*x

4. Multiply the derivative of the outer function by the derivative of the inner function.

−2*x⋅e^(−x^2)

Final Answer

d(e^(−x^2))/d(x)=−2*x*e^(−x^2)

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