Differentiation of a product check

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SUMMARY

The discussion focuses on differentiating the function s = 8sin(125t)e^-7t with respect to time t. The user correctly identifies u = 8sin(125t) and v = e^-7t, applying the product rule for differentiation. The derivative ds/dt is calculated as ds/dt = e^-7t * 1000cos(125t) + 8sin(125t) * -7e^-7t. The user seeks confirmation of the correctness of this solution, which is affirmed by other participants in the discussion.

PREREQUISITES
  • Understanding of calculus, specifically differentiation techniques.
  • Familiarity with the product rule in calculus.
  • Knowledge of trigonometric functions and their derivatives.
  • Basic understanding of exponential functions and their properties.
NEXT STEPS
  • Study the product rule in calculus in greater detail.
  • Explore the differentiation of trigonometric functions.
  • Learn about exponential decay and its applications in calculus.
  • Practice solving similar differentiation problems involving products of functions.
USEFUL FOR

Students studying calculus, educators teaching differentiation techniques, and anyone looking to improve their understanding of product rule applications in mathematical functions.

DBeckett91
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Homework Statement



s = 8sin(125t)e^-7t

Where the value of t is unknown

The Attempt at a Solution



u = 8sin(125t) du/dt = 1000cos(125t)

v = e^-7t dv/dt = -7e^-7t

ds/dt = v*du/dt + u*dv/dt

= (e^-7t * 1000cos(125t)) + (8sin(125t) * -7e^-7t)

Just need to know if my final answer is correct and if not where I have gone wrong. Thanks for any help that may be coming my way
 
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