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T(n)=33.55+77\cdot00.99^n

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Find derivatives using the quotient rule IIright chevron icon

Full solution

Q. T(n)=33.55+77\cdot00.99^n
  1. Identify Terms: Identify the constant term and the exponential term. T(n) = 3.53.5 + 7imes0.9n7 imes 0.9^n
  2. Derivative of Constant Term: The derivative of a constant term (\newline33.55\newline) is \newline00\newline. \newline\frac{d}{dn} [33.55] = 00\newline
  3. Chain Rule for Exponential Term: Use the chain rule to find the derivative of the exponential term. ddn[7⋅0.9n]=7⋅ddn[0.9n] \frac{d}{dn} [7 \cdot 0.9^n] = 7 \cdot \frac{d}{dn} [0.9^n]
  4. Apply Chain Rule: Apply the chain rule to the exponential term. ddn[0.9n]=0.9n⋅ln⁡(0.9) \frac{d}{dn} [0.9^n] = 0.9^n \cdot \ln(0.9)
  5. Combine Results: Combine the results. T′(n)=0+7imes0.9nimesextln(0.9)T'(n) = 0 + 7 imes 0.9^n imes ext{ln}(0.9)

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