what is the derivative of 2 raised to the power of x?

Answer 1

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

Answer 2

THE DERIVATIVE OF 2 RAISED TO THE POWER OF X IS 2*X1.e2X

Answer 3

derivative of 2^x = x [2^ (x-1)]

Answer 4

This one is tricky...
It is X Ln(2)

Which means its X Log(2) {to the base e - natural log}

Answer 5

u bring down the x multipy it by 2 and then it's x-1
so it's x[2^x-1] really easy to do these things...just do the same process

Answer 6

d/dx (2^x) = d/dx (e^ (ln2*x))=ln2*e^(ln2*x)=ln2*2^x

The first part used the following identity:

L^x=e^(lnL*x) (because e^(lnL*x)=(e^lnL)^x=L^x

The second part used the "chain rule"

d/dx(f(g(x))=df/dg * dg/dx

Therefore, d/dx(e^(ln2*x))=
d/dx(ln2*x)*d(e^(ln2*x)/d(ln2*x) =
ln2*(e^(ln2*x))=ln2 * 2^x
Nir

Answer 7

f(x) = 2^x = e^(xln2)
then f'(x) = ln2*e^(xln2) = ln2*2^x