Find the Derivative - d/dx e^(x^5)

Problem

d(e(x5))/d(x)

Solution

1. Identify the outer function as eu and the inner function as u=x5

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

3. Differentiate the inner function x5 using the power rule to get 5*x4

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

5. Simplify the resulting expression.

Final Answer

d(e(x5))/d(x)=5*x4*e(x5)

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