How do I take the partial derivative of P with respect to r of the following:

D �~ P = ‡”(t=1 to T)[t �~ (CF)_t/(1+r)^t ]

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Using the standard Western 8859-1, we do not see anything mathematical. Unicode does not help either.

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Using the standard Western 8859-1, we do not see anything mathematical. Unicode does not help either.

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To take the partial derivative of P with respect to r in the given expression, we can use the rules of calculus.

Step 1: Expand the summation
D × P = ∑[t × (CF)_t/(1+r)^t ]

Step 2: Differentiate term by term
To differentiate, we treat each term separately. The derivative of a constant term is zero, so we only need to focus on the terms involving (1+r)^t.

For each term, we can use the power rule of differentiation. The power rule states that if we have a term of the form (1+r)^t, the derivative with respect to r is t × (1+r)^(t-1).

Step 3: Apply the power rule
D × P = ∑[t × (CF)_t × t × (1+r)^(t-1)/(1+r)^t ]
= ∑[t × (CF)_t × (1+r)^(t-1)/(1+r)]

Step 4: Simplify the expression
To simplify the expression, we can rewrite (1+r)^(t-1)/(1+r) as (1+r)^(t-1-1) or (1+r)^(t-2).

D × P = ∑[t × (CF)_t × (1+r)^(t-2)]

This gives you the partial derivative of P with respect to r for the given expression.