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

Problem

d(2(x2))/d(x)

Solution

1. Identify the rule for differentiating an exponential function with base a which is d(au)/d(x)=au*ln(a)d(u)/d(x)

2. Apply the chain rule by setting u=x2 which means d(u)/d(x)=2*x

3. Substitute the components into the derivative formula.

4. Simplify the expression by rearranging the terms.

Final Answer

d(2(x2))/d(x)=2*x⋅2(x2)*ln(2)

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