Find the Derivative - d/dx e^(x^3)

Problem

d(e^(x^3))/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^3

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^3 using the Power Rule, which gives 3*x^2

4. Combine the results to find the final derivative.

Final Answer

d(e^(x^3))/d(x)=3*x^2*e^(x^3)

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