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education/math/MATH1210 (calc 1)/Derivatives.md
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@ -133,10 +133,11 @@ $$ \dfrac{d}{dx} \csc x = -\csc x \cot x $$
## Cotangent ## Cotangent
$$ \dfrac{d}{dx} \cot x = -\csc^2 x $$ $$ \dfrac{d}{dx} \cot x = -\csc^2 x $$
# Implicit Differentiation\ # Implicit Differentiation
- $\dfrac{d}{dx} * x^2 = \dfrac{d(x^2)}{dx}$, or, the derivative of $x^2$ with respect to x - There's a reason differentials are written like a fraction
- $\dfrac{dx}{dx} = 1$ : The derivative of $x$ with respect to $x$ is one - $\dfrac{d}{dx} x^2 = \dfrac{d(x^2)}{dx}$, or, "the derivative of $x^2$ with respect to $x$"
- - $\dfrac{d}{dx} x = \dfrac{dx}{dx} = 1$ : The derivative of $x$ with respect to $x$ is one
- $\dfrac{d}{dx} y = \dfrac{{dy}{dx} = y'$
# Examples # Examples
> Differentiate $f(x) = 4\sqrt[3]{x} - \dfrac{1}{x^6}$ > Differentiate $f(x) = 4\sqrt[3]{x} - \dfrac{1}{x^6}$