Find the Derivative - d/dx y=sin(4x)

Problem

d(sin(4*x))/d(x)

Solution

1. Identify the function as a composition of an outer function sin(u) and an inner function u=4*x

2. Apply the chain rule, which states that the derivative of ƒ*(g(x)) is ƒ′*(g(x))⋅g(x)′

3. Differentiate the outer function sin(u) with respect to u to get cos(u)

4. Differentiate the inner function 4*x with respect to x to get 4

5. Multiply the results together and substitute 4*x back in for u

Final Answer

d(sin(4*x))/d(x)=4*cos(4*x)

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