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 the derivative of e^ƒ(x) is e^ƒ(x) multiplied by the derivative of ƒ(x)

3. Differentiate the inner function x^2 using the Power Rule, which gives 2*x

4. Multiply the derivative of the outer function by the derivative of the inner function to find the final result.

Final Answer

d(e^(x^2))/d(x)=2*x*e^(x^2)

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