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

Problem

d(e(x2))/d(x)

Solution

1. Identify the outer function as eu and the inner function as u=x2

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

3. Differentiate the inner function x2 with respect to x using the power rule.

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

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

e(x2)⋅2*x

5. Rearrange the terms for standard mathematical notation.

2*x*e(x2)

Final Answer

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

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