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The dashes are actually roman numerals: the symbol for the forth order derivative would be a slanted IV.
The dashes are actually roman numerals: the symbol for the forth order derivative would be a slanted IV.
Picking up our earlier example;
Picking up our earlier example; <math>y = 3 x^2+2x</math>, the second derivative with respect to <math>x</math> is
:<math>\frac{d^{2}y}{dx^{2}} = \frac{d}{dx}(6 x+2)=6</math>
:<math>\frac{d^{3}y}{dx^{3}} = \frac{d}{dx}(6)=0</math>
All subsequent derivatives would be zero. For any [[polynomial]] of order n-1, <math>P_{n-1}(x)</math>,
:<math>\frac{d^{n}}{dx^{n}}P_{n-1}(x)=0</math>
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]].