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

Problem

d(sin(ex))/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=ex

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 ex with respect to x which results in ex

5. Multiply the results together and substitute u=ex back into the expression.

Final Answer

d(sin(ex))/d(x)=ex*cos(ex)

Want more problems? Check here!