Find the Derivative - d/dx e^(2x^2)

Problem

d(e(2*x2))/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=2*x2

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

3. Differentiate the inner function 2*x2 using the Power Rule.

(d(2)*x2)/d(x)=4*x

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

d(e(2*x2))/d(x)=e(2*x2)⋅4*x

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

d(e(2*x2))/d(x)=4*x*e(2*x2)

Final Answer

d(e(2*x2))/d(x)=4*x*e(2*x2)

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