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education/math/MATH1210 (calc 1)/Derivatives.md
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@ -108,7 +108,13 @@ $$ \dfrac{d}{dx} e^x = e^x $$
$$ \dfrac{d}{dx}a^x = a^x*(\ln(a)) $$ $$ \dfrac{d}{dx}a^x = a^x*(\ln(a)) $$
for all $a > 0$ 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 # Examples
> Differentiate $f(x) = 4\sqrt[3]{x} - \dfrac{1}{x^6}$ > Differentiate $f(x) = 4\sqrt[3]{x} - \dfrac{1}{x^6}$