Make a conjecture about the nth derivative of the function f(x)=e^(ax). This conjecture should be written as a self contained proposition including an appropriate quantifier.
Make a conjecture about the nth derivative of the function f(x)=e^(ax). This conjecture should be written as a self contained proposition including an appropriate quantifier.
That does this last sentence mean?
$\displaystyle f(x) = e^{ax}$
$\displaystyle f'(x) = ae^{ax}
$
$\displaystyle f''(x) = a^2e^{ax}$
$\displaystyle f'''(x) = a^3e^{ax}$
do you see a pattern to construct an expression for $\displaystyle f^{n}(x)$ so that you may answer within the given guidelines ?