Question

f(x) = ln(\sqrt{{9x+4}/sqrt{4x-2}})
find f'(x)

Answer 1

i got
\[\frac{\frac{1}{2}\!\left(9x+4\right)^{-\frac{1}{2}}\cdot 9}{\sqrt{9x+4}}-\frac{\frac{1}{2}\!\left(4x-2\right)^{\frac{-1}{2}}\cdot 4}{\sqrt{4x-2}}\]

Answer 2

but it says it's wrong

Answer 3

\[f \left( x \right)=\frac{ 1 }{ 2 }\left\{ \ln \left( 9x+4 \right)-\ln \left( 4x-2 \right) \right\}\]
\[f'\left( x \right)=\frac{ 1 }{2 }\left( \frac{ 9 }{9x+4 }-\frac{ 4 }{4x-2 } \right)\]

Answer 4

what about \[f(x) = 4^x \log_{7} (x)\]
will the answer be \[4^(x)*(1/\ln(7)*(1/x))\]

Answer 5

@surjithayer

Answer 6

diff taking uv functions.
d/dx(4^x)=4^x ln4

Answer 7

so it would be 4^(x)ln4*(1/ln(7)*(1/x))

Answer 8

d/dx(uv)=uv'+vu'
d/dx log7 (x)=1/x *log7( e)

Answer 9

thanks