Question

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

Answer 1

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

Answer 2

yes

Answer 3

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

Answer 4

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\[y′=b^u∗\ln(b)(du/dx)\]

Answer 5

yes i get it thank u so much

Answer 6

no problem