
• The power rule says $\dfrac {d}{dx}(x^n) = nx^{n-1}$.
• Exponential functions are of the form $f(x) = a^x$ and power functions are of the form $f(x) = x^n$, where $a$ is a positive real number and $n$ is an integer. The power rule only applies to differentiating a power function. There is a different formula for computing the derivative of an exponential function.
• The formula for differentiating an exponential function is $\dfrac {d}{dx}(a^x) = a^x \ln (a)$.
• The formula for differentiating a logarithmic function is $\dfrac {d}{dx}(\log _a(x)) = \dfrac {1}{x \ln (a)}$.
$\dfrac {d}{dx} \sin (x) = \cos (x)$
$\dfrac {d}{dx} \cos (x) = - \sin (x)$