Question

H(z)= 2^(1-6z)
find the derivative.
i started this but when i checked it on the calculator, i have no idea how it got the answer --12*ln(2)*(1/64)^x

Answer 1

-12* sorry i didnt mean to put - twice

Answer 2

let y = 2^(1-6z)
ln y = (1-6z) ln 2
dy/dz * 1/y = -6 ln 2
dy/dz = -6 ln 2 * y
= -6 ln 2 * 2 ^(1-6z)
= - 6 ln 2 *( 2^1 * 2 ^ -6z)
= -12 ln2 * (1/64^z)

Answer 3

is putting the ln automatically something i should of known about? O.o i feel like there are rules that i either dont know or have forgotten, that are making this seem much harder then what it really is.

Answer 4

you take logs ( ie ln) of each side when the unknown variable is in the exponent - in this case 1- 6z.
a simpler example is finder the derivative of 2^x:

let y = 2^x
then
ln y = ln 2^x
ln y = x ln 2
differentiate both sides:

dy/dx * 1/y = d (x ln 2) / dx
= ln 2
dy/dx = ln2 * y
= 2^x * ln 2

Answer 5

d (ln y) / dx = dy/dx * 1/y is by the chain rule

- the derivative of ln y = 1/y and derivative of y is dy/dx

Answer 6

derivative of y with respect to x is dy/dx

Answer 7

ooooh ok