Finding Derivative of y=5^(3-3x)

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SUMMARY

The derivative of the function y=5^(3-3x) can be calculated using the chain rule and the property of exponential functions. Specifically, the expression can be rewritten as y=e^{(3-3x) \ln 5}. Applying the chain rule, the derivative is found to be y' = -3 \ln(5) \cdot 5^{(3-3x)}. This method leverages the natural logarithm to simplify the differentiation process.

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  • Understanding of calculus, specifically differentiation techniques.
  • Familiarity with the chain rule in calculus.
  • Knowledge of exponential functions and their properties.
  • Basic understanding of natural logarithms.
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  • Study the chain rule in calculus for more complex derivatives.
  • Learn about the properties of exponential functions, particularly with different bases.
  • Explore the application of natural logarithms in calculus.
  • Practice finding derivatives of various exponential functions.
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Students studying calculus, educators teaching differentiation, and anyone looking to refresh their knowledge on exponential functions and derivatives.

chantella28
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Hey guys,
I have a calculus problem that should be easy but I haven't taken calc in a few years so I can't remember where to begin. If somebody could give me some help with this, that would be great

find the following derivative: y=5^(3-3x)
 
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You know the derivative of e^x and the chain rule (right?), so just use these along with the fact that:

[tex]5^{a}=e^{a \ln 5}[/tex]
 

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