Simply Math

Definition and Notation

If \( y = f(x) \) then the derivative is defined to be \( f' (x) = \mathop {\lim }\limits_{h \to 0} \frac{{f\left( x + h \right) - f\left( x \right)}}{{h}} \)

If \(y = f ( x)\)  then all of the following are equivalent notations for the derivative.

\( f'(x) = y' = \frac{df}{dx} = \frac{dy}{dx} = \frac{d}{dx} = (f(x)) = Df(x) \)

Common Derivatives

Example: \( \frac{d}{dx}(sin x) = cos x \)

Example: \( \frac{d}{dx}(sin^{-1} x) = \frac{1}{ \sqrt{1+x^2} } \)