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education/math/MATH1210 (calc 1)/Derivatives.md
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@ -137,7 +137,8 @@ $$ \dfrac{d}{dx} \cot x = -\csc^2 x $$
- There's a reason differentials are written like a fraction - There's a reason differentials are written like a fraction
- $\dfrac{d}{dx} x^2 = \dfrac{d(x^2)}{dx}$, or, "the derivative of $x^2$ with respect to $x$" - $\dfrac{d}{dx} x^2 = \dfrac{d(x^2)}{dx}$, 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 - $\dfrac{d}{dx} x = \dfrac{dx}{dx} = 1$ : The derivative of $x$ with respect to $x$ is one
- $\dfrac{d}{dx} y = \dfrac{{dy}{dx} = y'$ - $\dfrac{d}{dx} y = \dfrac{dy}{dx} = y'$
- Given the equation $y = x^2$, $\dfrac{d}{dx} y = \dfrac{dy}{dx} = 2x$.
# Examples # Examples
> Differentiate $f(x) = 4\sqrt[3]{x} - \dfrac{1}{x^6}$ > Differentiate $f(x) = 4\sqrt[3]{x} - \dfrac{1}{x^6}$