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anonymous

  • 5 years ago

help pls " find Derivative of g(x)=3^(2x+7)

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  1. anonymous
    • 5 years ago
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    is this function you have to differentiate?\[g(x)=3^{2x+7}\]

  2. anonymous
    • 5 years ago
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    yes

  3. anonymous
    • 5 years ago
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    \[y=b^u \rightarrow dy/dx=b^ulnb(du/dx)\] in your case: \[g=3^{2x+7}\rightarrow u=2x+7,b=3, du=2dx, du/dx=2\] \[dg/dx=3^{2x+7}*\ln(3)*2\]

  4. anonymous
    • 5 years ago
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    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\[y′=b^u∗\ln(b)(du/dx)\]

  5. anonymous
    • 5 years ago
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    yes i get it thank u so much

  6. anonymous
    • 5 years ago
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    no problem

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