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derivative of $275.33S - S \ln S \times \frac{1}{0.015}$

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Convert rates and measurements: metric units

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Q. derivative of

275.33S - S \ln S \times \frac{1}{0.015}

Simplify Expression: First, let's simplify the expression by distributing the multiplication across the terms. $\newline$ $275.33S - S \ln(S) \times \frac{1}{0.015} = 275.33S - \frac{S \ln(S)}{0.015}$
Find Derivatives: Now, let's find the derivative of each term separately. $\newline$ The derivative of $275.33S$ with respect to $S$ is $275.33$ .
Apply Product Rule: Next, we need to apply the product rule to the term $-\frac{S \ln(S)}{0.015}$ , since it is the product of $S$ and $\ln(S)$ . Let $u = S$ and $v = \ln(S)$ . Then $\frac{du}{dS} = 1$ and $\frac{dv}{dS} = \frac{1}{S}$ . Using the product rule $\left(\frac{d(uv)}{dS} = u \frac{dv}{dS} + v \frac{du}{dS}\right)$ , we get: \frac{d(-S \ln(S) / \(0\).\(015\))}{dS} = -\frac{\(1\)}{\(0\).\(015\)} * \left(S * \left(\frac{\(1\)}{S}\right) + \ln(S) * \(1\right)
Simplify Derivative: Simplify the derivative we just found. $\newline$ $-\frac{1}{0.015} * (S * (\frac{1}{S}) + \ln(S) * 1) = -\frac{1}{0.015} * (1 + \ln(S))$
Combine Derivatives: Combine the derivatives of both terms to get the final derivative of the function. $\newline$ $\frac{d(275.33S - S \ln(S) \times \frac{1}{0.015})}{dS} = 275.33 - \frac{1}{0.015} \times (1 + \ln(S))$
Calculate Numerical Value: Now, let's calculate the numerical value of $-\frac{1}{0.015}$ to simplify the expression. $\newline$ $-\frac{1}{0.015} = -66.666\ldots$

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