vault backup: 2025-02-09 16:35:33

education/math/MATH1210 (calc 1)/Derivatives.md

@@ -109,12 +109,20 @@ $$ \dfrac{d}{dx}a^x = a^x*(\ln(a)) $$
 for all $a > 0$
 
 # Trig Functions
-
+$$ \lim_{x \to 0} \dfrac{\sin x}{x} = 1 $$
+$$ \lim_{x \to 0} \dfrac{\cos x - 1}{x} = 0 $$
 ## 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
+This allows us to simplify, ultimately leading to:
+$$ \dfrac{d}{dx} \sin x = \cos x$$
+## Cosine
+$$ \dfrac{d}{dx} \cos x = -\sin x $$
+
+## Tangent
+$$ \dfrac{1}{\cos^2x}$$
+
 # Examples
 
 > Differentiate $f(x) = 4\sqrt[3]{x} - \dfrac{1}{x^6}$