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

Problem

d(esin(2*x))/d(x)

Solution

1. Identify the outer function as eu and the inner function as u=sin(2*x)

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

3. Differentiate the inner function u=sin(2*x) by applying the chain rule again.

4. Calculate the derivative of sin(2*x) as cos(2*x)⋅(d(2)*x)/d(x)

5. Simplify the derivative of 2*x to 2

6. Combine all parts to find the final derivative.

Final Answer

d(esin(2*x))/d(x)=2*cos(2*x)*esin(2*x)

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