Find the Derivative - d/dx e^(4x^3)

Problem

d(e^(4*x^3))/d(x)

Solution

1. Identify the outer function as e^u and the inner function as u=4*x^3

2. Apply the chain rule, which states that d(e^u)/d(x)=e^u⋅d(u)/d(x)

3. Differentiate the inner function 4*x^3 using the power rule to get 12*x^2

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

5. Simplify the resulting expression.

Final Answer

d(e^(4*x^3))/d(x)=12*x^2*e^(4*x^3)

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