Find the Derivative - d/dZ sin(x)

Problem

d(sin(x))/d(Z)

Solution

1. Identify the variable of differentiation and the variable in the expression. The task asks for the derivative with respect to Z but the function is sin(x)

2. Determine if x is a function of Z In standard calculus notation, if x is an independent variable distinct from Z it is treated as a constant.

3. Apply the constant rule for derivatives. The derivative of any constant with respect to a variable is 0

4. Consider the chain rule if x is an implicit function of Z If x depends on Z the derivative would be cos(x)d(x)/d(Z) However, without an explicit relationship provided, x is treated as a constant relative to Z

Final Answer

d(sin(x))/d(Z)=0

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