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

Problem

d(e(x4))/d(x)

Solution

1. Identify the outer function and the inner function to apply the Chain Rule. The outer function is eu and the inner function is u=x4

2. Apply the Chain Rule which states that d(eu)/d(x)=eu⋅d(u)/d(x)

3. Differentiate the inner function x4 using the Power Rule.

d(x4)/d(x)=4*x3

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

d(e(x4))/d(x)=e(x4)⋅4*x3

5. Rearrange the terms to write the expression in standard form.

d(e(x4))/d(x)=4*x3*e(x4)

Final Answer

d(e(x4))/d(x)=4*x3*e(x4)

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