Find the Derivative - d/dx cos(6x)

Problem

d(cos(6*x))/d(x)

Solution

1. Identify the outer function as cos(u) and the inner function as u=6*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 cos(u) with respect to u to get −sin(u)

4. Differentiate the inner function 6*x with respect to x to get 6

5. Multiply the results together and substitute 6*x back for u

Final Answer

d(cos(6*x))/d(x)=−6*sin(6*x)

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