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

Problem

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

Solution

1. Identify the rule needed for the derivative of an exponential function with a composite exponent.

2. Apply the chain rule, which states that the derivative of eu is eu⋅d(u)/d(x)

3. Set u=4*x and find its derivative.

4. Calculate the derivative of 4*x which is 4

5. Multiply the original exponential function by the derivative of the exponent.

Final Answer

d(e(4*x))/d(x)=4*e(4*x)

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