Find the Derivative - d/dx f(x)=cos((pix)/2)

Problem

d()/d(x)*cos((π*x)/2)

Solution

1. Identify the outer function as cos(u) and the inner function as u=(π*x)/2

2. Apply the chain rule, which states that d(cos(u))/d(x)=−sin(u)⋅d(u)/d(x)

3. Differentiate the inner function (π*x)/2 with respect to x which results in the constant π/2

4. Multiply the derivative of the outer function by the derivative of the inner function.

5. Simplify the expression by placing the constant coefficient at the front.

Final Answer

d(cos((π*x)/2))/d(x)=−π/2*sin((π*x)/2)

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