Find the Derivative - d/dx cos(5x)

Problem

d(cos(5*x))/d(x)

Solution

1. Identify the outer function as cos(u) and the inner function as u=5*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 5*x with respect to x to get 5

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

6. Simplify the final expression by moving the constant to the front.

Final Answer

d(cos(5*x))/d(x)=−5*sin(5*x)

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