diff --git a/education/math/MATH1210 (calc 1)/Derivatives.md b/education/math/MATH1210 (calc 1)/Derivatives.md index 4164486..e780f14 100644 --- a/education/math/MATH1210 (calc 1)/Derivatives.md +++ b/education/math/MATH1210 (calc 1)/Derivatives.md @@ -108,7 +108,13 @@ $$ \dfrac{d}{dx} e^x = e^x $$ $$ \dfrac{d}{dx}a^x = a^x*(\ln(a)) $$ for all $a > 0$ +# Trig Functions +## Sine +$$ f'(x) = \lim_{h \to 0} \dfrac{\sin(x + h) - sin(x)}{h} $$ +Using the sum trig identity, $\sin(x + h)$ can be rewritten as $\sin x \cos h + \cos x \sin h$. + +This allows us to simplify, ul # Examples > Differentiate $f(x) = 4\sqrt[3]{x} - \dfrac{1}{x^6}$