How do I eliminate the arbitrary constant A from the function: y = Ae^(3x)?
Here is my attempt:
y = Ae^(3x)
dy/dx = (how do I differentiate Ae^(3x) ) ??
$\displaystyle e^x$ is the world's easiest function to differentiate! Its derivative is just itself, $\displaystyle e^x$. To differentiate $\displaystyle e^{3x}$, use the chain rule to get the derivative dwsmith did.
To get an equation that does not involve the constant A, divide the derivative of y by y:
$\displaystyle \frac{dy}{dx}= \frac{3Ae^{3x}}{Ae^{3x}}= 3$.