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education/math/MATH1210 (calc 1)/Derivatives.md
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@ -37,6 +37,9 @@ Given the equation $y = f(x)$, the following are all notations used to represent
# Higher Order Derivatives # Higher Order Derivatives
- Take the derivative of a derivative - Take the derivative of a derivative
# Constant Rule
The derivative of a constant is always zero.
# Exponential Derivative Formula # Exponential Derivative Formula
Using the definition of a derivative to determine the derivative of $f(x) = x^n$, where $n$ is any natural number. Using the definition of a derivative to determine the derivative of $f(x) = x^n$, where $n$ is any natural number.
@ -91,4 +94,4 @@ $$ \dfrac{d}{dx}(\dfrac{f(x)}{g(x)}) = \dfrac{f'(x)g(x) -f(x)g'(x)}{(g(x))^2} $
# Exponential Rule # Exponential Rule
$$ \dfrac{d}{dx} e^x = e^x $$ $$ \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 $a > 0$