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

Problem

d()/d(x)*sin(π*x)

Solution

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

2. Apply the chain rule, which states that the derivative of sin(u) is cos(u)⋅d(u)/d(x)

3. Differentiate the inner function π*x with respect to x which results in π

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

Final Answer

d(sin(π*x))/d(x)=π*cos(π*x)

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