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

Problem

d(sin(e^x))/d(x)

Solution

1. Identify the outer function and the inner function to apply the Chain Rule. The outer function is sin(u) and the inner function is u=e^x

2. Apply the Chain Rule which states that (d(ƒ)*(g(x)))/d(x)=ƒ^′*(g(x))⋅g(x)^′

3. Differentiate the outer function sin(u) with respect to u which results in cos(u)

4. Differentiate the inner function e^x with respect to x which results in e^x

5. Multiply the results together and substitute u=e^x back into the expression.

Final Answer

d(sin(e^x))/d(x)=e^x*cos(e^x)

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