Question

how would i differentiate this?
y=3.9657(0.9982^x)

Answer 1

d(a^x)=a^x*lna dx

Answer 2

would it be y'=3.9657(0.9982^x) ln0.9982 ?

Answer 3

\[\frac{d}{dx}a^x=a^x \times \log_{e}a=a^x \times \ln a\]

Answer 4

do you know why it's like that??

Answer 5

yes, you can arrive at the formula by applying log to both the sides

Answer 6

@Nishant_Garg actually i didn't meant you :)

Answer 7

yes i do thanks! also to find the instantaneous rate of change (i am given a table of values) would I just sub in the x values?

Answer 8

Oh my bad

Answer 9

yea

Answer 10

cool thanks!