Question

Find k such that 9^x = e^(k x) for all values of x.

I found K =LN(9)

BUT,Then use your result to find the derivative of y = 9^x = e^(k x)

Answer 1

i found y'= 9^x=e^((ln9)*x) but dont know if its right

Answer 2

what is your y'

Answer 3

9^x=e^((ln9)*x)

Answer 4

thats my answer

Answer 5

thats just the originalequation with k replaced so you needto fid the derivative of that

Answer 6

i just plugged in ln(9) for k

Answer 7

oh ok how do i find the derivative then?

Answer 8

derivative of e^(some constatn*x)=some constant*e^(some constant * x)

Answer 9

product rule?

Answer 10

im kinda lost

Answer 11

the exponent rule

Answer 12

for when x is the exponent

Answer 13

could u write it out?

Answer 14

ln(9)*e^(x*ln(9))

Answer 15

so what is e?

Answer 16

the deriv of ln(9) is what?

Answer 17

e is a very special non-repeating constant number

Answer 18

derivative of ln(9) would be 0 since its a constant

Answer 19

so it would be just x

Answer 20

or e^x =1

Answer 21

c=some constant number
the derivative of e^(cx)=c*e^(cx)

Answer 22

whats the constant number?

Answer 23

ln(9) is a constant number. A constant is anything in the equation tha doesnt contain a variable

Answer 24

ok