Difference between revisions of "Derivative/Formulas"
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− | | <math>\frac d{dx}(cf(x)) = c\left(\frac d{dx} f(x)\right)</math> where c is a constant | + | | <math>\frac d{dx}(cf(x)) = c\left(\frac d{dx} f(x)\right)</math> where <math>c</math> is a constant |
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| <math>(f(x) + g(x))' = f'(x) + g'(x)</math> | | <math>(f(x) + g(x))' = f'(x) + g'(x)</math> | ||
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| <math>\frac d{dx} \arctan x = \frac 1{1+x^2}</math> | | <math>\frac d{dx} \arctan x = \frac 1{1+x^2}</math> | ||
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− | | <math>\frac d{dx} \mathrm{arcsec \ } x = \frac 1{\ | + | | <math>\frac d{dx} \mathrm{arcsec \ } x = \frac 1{\lvert x \rvert \sqrt{x^2-1}}</math> |
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| <math>\frac d{dx} \mathrm{arccsc \ } x = - \frac 1{x\sqrt{x^2 - 1}}</math> | | <math>\frac d{dx} \mathrm{arccsc \ } x = - \frac 1{x\sqrt{x^2 - 1}}</math> |
Latest revision as of 16:23, 11 March 2022
List of formulas
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Notation
The following are commonly recognized notations for expressing the derivative of a function.
Euler's notation | |
First derivative | ![]() ![]() |
Second derivative | ![]() ![]() |
Third derivative | ![]() ![]() |
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Lagrange's notation | |
First derivative | ![]() |
Second derivative | ![]() |
Third derivative | ![]() |
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Leibniz's notation | |
First derivative | ![]() |
Second derivative | ![]() |
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Newton's notation | |
First derivative | ![]() |
Second derivative | ![]() |