diff --git a/education/math/MATH1210 (calc 1)/Derivatives.md b/education/math/MATH1210 (calc 1)/Derivatives.md index 9301784..c24f9bf 100644 --- a/education/math/MATH1210 (calc 1)/Derivatives.md +++ b/education/math/MATH1210 (calc 1)/Derivatives.md @@ -67,8 +67,8 @@ $$ \lim_{h \to 0} nx^{n-1} + P_{n3} x^{n-2}*0 \cdots v * 0 $$ The zeros leave us with: $$ f(x) = n, \space f'(x) = nx^{n-1} $$ -# Addition/Subtraction Derivative Rule -You can add and subtract derivatives to find what the derivative of the whole derivative would be. +# Sum and Difference Rules +$$ \dfrac{d}{dx}(f(x) \pm g(x)) = f'(x) \pm g'(x) $$ # Product Rule $$ \dfrac{d}{dx} (f(x) * g(x)) = \lim_{h \to 0} \dfrac{f(x +h) * g(x + h) - f(x)g(x)}{h} $$ @@ -81,4 +81,6 @@ 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: -$$ \dfrac{d}{dx}(f(x) * g(x)) = f(x) * g'(x) + f'(x)* \ No newline at end of file +$$ \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