Question

f(x)=2^xradical x

Answer 1

\[2^{x}\sqrt{x}\]

Answer 2

this is another product rule problem

Answer 3

this time

f(x) = 2^x
g(x) = sqrt(x)

Answer 4

it turns out that \[\Large \sqrt{x} = x^{1/2}\]

Answer 5

so g(x) = x^(1/2)

with me so far?

Answer 6

thats a general rule? x^1/2?

Answer 7

yes the general rule is that \[\Large \sqrt{x} = x^{1/2}\]

Answer 8

i was able to get to 1/2radical x

Answer 9

then I'm lost

Answer 10

To derive 2^x, you use the rule that

if

\[\Large f(x) = b^x\]

then

\[\Large f^{\prime}(x) = b^x*\ln(b)\]

Answer 11

in this case, b = 2, so

\[\Large f(x) = 2^x\]

turns into

\[\Large f^{\prime}(x) = 2^x*\ln(2)\]

Answer 12

I think the website is glitched because I dont see the equations like I usually can

Answer 13

oh so you only see the code?

Answer 14

yes unfortunately

Answer 15

hmm that sucks, ok I'll draw it out

Answer 16

if