Question

find the derivative

Answer 1

\[y=3^\tan \theta \ln3\]

Answer 2

did you look under the parsley?

Answer 3

lol

Answer 4

the theta sing should be in the exponent like 3^tan theta

Answer 5

\[y=3^{\tan(\theta)} \ln(3)\]?

Answer 6

yep thats the one

Answer 7

first of all
\[ln(3)\] is a constant. so just leave it there

Answer 8

okay can you explai why its a constant?

Answer 9

then recall that the derivative if
\[b^x\] is
\[b^x\times \ln(b)\]

Answer 10

okay

Answer 11

sure.
\[\ln(3)\] is a constant because 3 is a number

Answer 12

right

Answer 13

hey sensei!

Answer 14

so \[ln(3) is also a number

Answer 15

hello guru!

Answer 16

lol

Answer 17

new moniker?

Answer 18

yes

Answer 19

@mathcruncher let's finish
the derivative of
\[b^x\] is \[b^x\times \ln(b)\] so via the chain rule the derivative of
\[3^{\tan(\theta)}\]
is
\[3^{\tan(\theta)} \times \sec^2(\theta)\times \ln(3)\]

Answer 20

i guess you have to multiply this whole thing by
\[\ln(3)\] and be done

Answer 21

@my myininaya
\[\color{#ff0099}{\text{congratulations!}}\]

Answer 22

:)

Answer 23

wait so waht would be the final anser?

Answer 24

you are probably the only guru here!

Answer 25

i guess it would be
\[\sec^2(\theta)\times \ln^2(3)\times 3^{\tan(\theta)}\]

Answer 26

wouldnt the 3^tan theta also get multiplied by ln 3

Answer 27

as well as the sec^2 theta