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

Jun 16, 2018

$\frac{{e}^{2 x} \left(1 - \ln \left(2\right)\right)}{{2}^{2 x - 1}}$

#### Explanation:

After the Quotient rule

$\left(\frac{u}{v}\right) ' = \frac{u ' v - u v '}{v} ^ 2$

we get

$f ' \left(x\right) = \frac{{e}^{2 x} 2 \cdot {4}^{x} - {e}^{2 x} \cdot {4}^{x} \cdot \ln \left(4\right)}{{4}^{x}} ^ 2$
simplifying we get

$\frac{{e}^{2 x} \left(1 - \ln \left(2\right)\right)}{{2}^{4 x - 2 x - 1}}$
and this is equal to

$\frac{{e}^{2 x} \left(1 - \ln \left(2\right)\right)}{{2}^{2 x - 1}}$