Log/Exponential Functions (Leaving Cert Mathematics): Flashcards

$f(x) = 2^x$ is an exponential function.

The derivative of $\ln(x)$ is $\frac{1}{x}$.

The derivative of $e^x$ is $e^x$.

The derivative is $ae^{ax}$.

The derivative is $a^x \ln(a)$.

It helps differentiate composite functions.

Identify $v=\sin(x)$, $u=e^v$, then differentiate.

$v' = \cos(x)$.

$u' = e^v$.

Result is $\cos(x)e^{\sin(x)}$.