diff --git a/education/math/MATH1210 (calc 1)/Derivatives.md b/education/math/MATH1210 (calc 1)/Derivatives.md index c24f9bf..4a8d12d 100644 --- a/education/math/MATH1210 (calc 1)/Derivatives.md +++ b/education/math/MATH1210 (calc 1)/Derivatives.md @@ -81,6 +81,13 @@ Then break into two different fractions: $$\lim_{h \to 0} \dfrac{f(x + h)}{1} * \dfrac{(g(x + h) - g(x))}{h)} + \dfrac{g(x)}{1} *\dfrac{f(x + h) - f(x)}{h} $$ From here, you can take the limit of each fraction, therefore showing that to find the derivative of two values multiplied together, you can use the formula: -$$ \dfrac{d}{dx}(f(x) * g(x)) = f(x) * g'(x) + f'(x) $$ -# Natural Exponential Function -$$ \dfrac{d}{dx} e^x = e^x $$ \ No newline at end of file +$$ \dfrac{d}{dx}(f(x) * g(x)) = f(x) * g'(x) + f'(x)*g(x) $$ + +# Constant Multiple Rule +$$ \dfrac{d}{dx}[c*f(x)] = c * f'(x) $$ +# Quotient Rule +$$ \dfrac{d}{dx}(\dfrac{f(x)}{g(x)}) = \dfrac{f'(x)g(x) -f(x)g'(x)}{(g(x))^2} $$ + +# Exponential Rule +$$ \dfrac{d}{dx} e^x = e^x $$ +$$ \dfrac{d}{dx}a^x \ No newline at end of file