Question

differentiate

y = (2x+5)^x

Answer 1

do know ln and e

Answer 2

would it be e^(xln(2x+5))

Answer 3

if so i didnt know how to go from there

Answer 4

you can right like this
\[\ln y=\ln (2x+5)^x\]
\[\ln y=x \ln (2x+5)\]

Answer 5

oh yeah

Answer 6

i'm always forgetful

Answer 7

from there it would be chain rule right??

Answer 8

yes

Answer 9

okay i did chain rule and i got

x/(2x+5) + ln(2x+5)

this is wrong though

Answer 10

that is correct but the thing is the other side of the equation is still ln y

Answer 11

right but when i did wolfram they got

(2x+5)^5 * ( 2x/(2x+5) + ln(2x+5) )

Answer 12

using implicit differentiation
\[f(x) = \ln y\]
\[f(x)\prime =y \prime/y\]
and
\[y \prime /(2x+5)^x=x/(2x+5) + \ln(2x+5)\]

Answer 13

so to get the derivative finally we have to multiply with (2x+5)^x

Answer 14

shouldn't it be 2x/2x+5 instead of x/2x+5

Answer 15

the first one ofcourse but did you get the implicit differentiation part

Answer 16

yes