by Diane Holcomb | Oct 10, 2024 | Calculus, Math
Derivatives of exponentials summary The derivative of $e^x$ The derivative of $e^x$ is $$frac{d}{dx} Big( e^x Big) = e^x.$$ We can prove this by going back to the definition. $$begin{eqnarray} frac{d}{dx} Big( e^x Big) &= lim_{hto 0} frac{e^{x+h}-e^x}{h}\ &...
by Diane Holcomb | Oct 8, 2024 | Calculus, Math
The antiderivative of 1/x Finding the integral of 1/x Because we can see that $frac{1}{x}$ can be written as $x^{-1}$ we’re always tempted to look at the power rule for integration to determine it’s integral, but we can see right away that this...
by Diane Holcomb | Sep 23, 2024 | Calculus, Math
Trig derivatives summary The derivative of sin x The derivative of $sin x$ is $$frac{d}{dx} left( sin x right) = cos x.$$ We can prove this by going back to the definition. $$frac{d}{dx} left( sin x right) = lim_{hto 0} frac{sin (x+h)-sin x}{h}.$$ The first thing we...
