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monroe17

  • 3 years ago

derivative y=(2)^(5x+3)

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  1. hartnn
    • 3 years ago
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    can you derivate a^x ?

  2. monroe17
    • 3 years ago
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    I'm not sure.. I need help like step by step through it too btw.

  3. hartnn
    • 3 years ago
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    yes, do u know what is chain rule ?

  4. monroe17
    • 3 years ago
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    yes. A'(B)*B'

  5. hartnn
    • 3 years ago
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    thats correct. now, \(\huge \frac{d}{dx}a^x=a^x\ln a\) so what will be derivative of 2^(5x+3) =?

  6. monroe17
    • 3 years ago
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    2^(5x+3)*ln(2)

  7. hartnn
    • 3 years ago
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    let me give you 1st step, \(y=2^{5x+3} \\ \text{differentiate both sides w.r.t x} \\ y'=2^{5x+3}\ln2(5x+3)' \quad \text{using chain rule, got this ?}\)

  8. hartnn
    • 3 years ago
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    \(y'=2^{5x+3}(\ln2)(5x+3)'=? \)

  9. monroe17
    • 3 years ago
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    5ln(2)(2)^(5x+3)

  10. hartnn
    • 3 years ago
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    absolutely correct! thats your final answer....

  11. hartnn
    • 3 years ago
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    did u understand ?

  12. monroe17
    • 3 years ago
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    oh thanks! ;D

  13. monroe17
    • 3 years ago
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    yeah :) it makes more sense now!

  14. hartnn
    • 3 years ago
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    welcome ^_^

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