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→Higher order derivatives
:<math>\frac{d^{3}y}{dx^{3}}=\frac{d}{dx}\left(\frac{d^{2}y}{dx^{2}}\right)=\frac{d}{dx}\left(\frac{d}{dx}\left(\frac{dy}{dx}\right)\right)</math>
:<math>\frac{d^{3}y}{dx^{3}}=\frac{d}{dx}\left(\frac{d^{2}y}{dx^{2}}\right)=\frac{d}{dx}\left(\frac{d}{dx}\left(\frac{dy}{dx}\right)\right)</math>
and so forth.
and so forth. The derviatives are termed the n-th order derivative e.g, second order derivative, third order derivative.
A common alternative notation is,
:<math>\frac{d^{2}y}{dx^{2}}=f''(x)</math>
:<math>\frac{d^{3}y}{dx^{3}}=f'''(x)</math>
:<math>\frac{d^{n}y}{dx^{n}}=f^{n}(x)</math>
The dashes actually roman numerals the symbol for the forth order derivative would be a slanted IV.
Other than the second derivative these have no real applications{{fact}}. A function which is differentiable infinite times is termed a [[smooth function]].
Other than the second derivative these have no real applications{{fact}}. A function which is differentiable infinite times is termed a [[smooth function]].