## anonymous 5 years ago help pls " find Derivative of g(x)=3^(2x+7)

1. anonymous

is this function you have to differentiate?$g(x)=3^{2x+7}$

2. anonymous

yes

3. anonymous

$y=b^u \rightarrow dy/dx=b^ulnb(du/dx)$ in your case: $g=3^{2x+7}\rightarrow u=2x+7,b=3, du=2dx, du/dx=2$ $dg/dx=3^{2x+7}*\ln(3)*2$

4. 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$y′=b^u∗\ln(b)(du/dx)$

5. anonymous

yes i get it thank u so much

6. anonymous

no problem