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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:
-$$ \dfrac{d}{dx}(f(x) * g(x)) = f(x) * g'(x) + f'(x)*
+$$ \dfrac{d}{dx}(f(x) * g(x)) = f(x) * g'(x) + f'(x) $$
+# Natural Exponential Function
+$$ \dfrac{d}{dx} e^x = e^x $$