Question

find the derivative step by step of y = 2^x

Answer 1

y = x^(2x)
==> ln(y) = ln[x^(2x)]
==> ln(y) = 2x*ln(x).

Then by logarithmic differentiation and the Product Rule:

1/y * dy/dx = 2ln(x) + 2x(1/x)
==> 1/y * dy/dx = 2[ln(x) + 1]
==> dy/dx = 2y * [ln(x) + 1]
==> dy/dx = 2 * x^(2x) * [ln(x) + 1].

Answer 2

lake logs:
ln y = ln 2^x

now differentiate both sides and simplify

Answer 3

blast - is yore first line correc?

Answer 4

ny = 2x*lnx
1/y dy/dx = 2lnx + 2
dy/dx = 2y(lnx + 1)

dy/dx = 2* x^(2x) * (lnx + 1)

Answer 5

Thanx for correcting me

Answer 6

THATS OK