Question

what is the derivative of (sin(e))^x

Answer 1

the deriv of sin(x) is cos(x) and solve as a chain rule

Answer 2

the derivative of e^x is e^x

Answer 3

the answer is ln(sin(e)) (sin(e))^x but how do you get to this

Answer 4

@asong195 , The x isn't the power of e , but the whole thing.

Answer 5

assume you have

y = u^v take ln for both sides

lny = vlnu (derive)

y'/y = v'lnu + v * u'/u

y = u^v

y' = u^v v' ln u + v * u^(v-1) * u'

Answer 6

You can use the last formula for deriving or add ln yourself.

Answer 7

y = (sin(e))^x

ln y = x lnsin(e) (notice that lnsine is a constant)

y'/y= lnsin(e) (from the main y)

y' = ylnsin(e) = (sin(e))^x * lnsin(e)

Answer 8

how come you don't derive lnsin(e)