anonymous
  • anonymous
help pls " find Derivative of g(x)=3^(2x+7)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
is this function you have to differentiate?\[g(x)=3^{2x+7}\]
anonymous
  • anonymous
yes
anonymous
  • anonymous
\[y=b^u \rightarrow dy/dx=b^ulnb(du/dx)\] in your case: \[g=3^{2x+7}\rightarrow u=2x+7,b=3, du=2dx, du/dx=2\] \[dg/dx=3^{2x+7}*\ln(3)*2\]

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anonymous
  • anonymous
do you understand how I got the answer? \[y=b^u \rightarrow lny=lnb^u \rightarrow lny=ulnb\] now differentiate with respect to y and you get: \[(1/y)y'=\ln(b)du/dx \rightarrow y'=y*\ln(b)du/dx\] since we know what y is, we can substitute it back in for the differential equation giving\[y′=b^u∗\ln(b)(du/dx)\]
anonymous
  • anonymous
yes i get it thank u so much
anonymous
  • anonymous
no problem

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