anonymous
  • anonymous
derivative y=(2)^(5x+3)
Mathematics
katieb
  • katieb
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hartnn
  • hartnn
can you derivate a^x ?
anonymous
  • anonymous
I'm not sure.. I need help like step by step through it too btw.
hartnn
  • hartnn
yes, do u know what is chain rule ?

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anonymous
  • anonymous
yes. A'(B)*B'
hartnn
  • hartnn
thats correct. now, \(\huge \frac{d}{dx}a^x=a^x\ln a\) so what will be derivative of 2^(5x+3) =?
anonymous
  • anonymous
2^(5x+3)*ln(2)
hartnn
  • hartnn
let me give you 1st step, \(y=2^{5x+3} \\ \text{differentiate both sides w.r.t x} \\ y'=2^{5x+3}\ln2(5x+3)' \quad \text{using chain rule, got this ?}\)
hartnn
  • hartnn
\(y'=2^{5x+3}(\ln2)(5x+3)'=? \)
anonymous
  • anonymous
5ln(2)(2)^(5x+3)
hartnn
  • hartnn
absolutely correct! thats your final answer....
hartnn
  • hartnn
did u understand ?
anonymous
  • anonymous
oh thanks! ;D
anonymous
  • anonymous
yeah :) it makes more sense now!
hartnn
  • hartnn
welcome ^_^

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