Question

How do you find the derivative of `(e^(2x))/(4^x)`?

Answer 1

`(e^(2x)(1-ln(2)))/(2^(2x-1))`

Explanation:

After the Quotient rule

`(u/v)'=(u'v-uv')/v^2`

we get

`f'(x)=(e^(2x)2*4^x-e^(2x)*4^x*ln(4))/(4^x)^2`
simplifying we get

`(e^(2x)(1-ln(2)))/(2^(4x-2x-1))`
and this is equal to

`(e^(2x)(1-ln(2)))/(2^(2x-1))`