Find the Derivative - d/dx f(x)=p^3

Problem

d(p3)/d(x)

Solution

1. Identify the variable of differentiation and the variable in the expression. The task asks for the derivative with respect to x but the expression is p3

2. Determine if p is a constant or a function of x In standard calculus notation, if p is not specified as a function of x it is treated as a constant.

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

4. Consider the case of implicit differentiation. If p were a function of x the chain rule would result in 3*p2d(p)/d(x) However, without that specification, we treat p as a constant.

Final Answer

d(p3)/d(x)=0

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