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Differentials
The following general rules can be applied to all differentials, where f() and g() are functions.
| d/dx( n f(x) ) | = | n d/dx( f(x) ) |
| d/dx( f(x) + g(x) ) | = | d/dx( f(x) ) + d/dx( g(x) ) |
| d/dx( f(x) g(x) ) | = | f(x) d/dx( g(x) ) + g(x) d/dx( f(x) ) |
| d/dx( f(x) / g(x) ) | = | ( g(x) d/dx( f(x) ) - f(x) d/dx( g(x) ) ) / g2(x) |
| d/dx( f( g(x) ) | = | d/dg( f(x) ) d/dx( g(x) ) |
Differentials of Common Functions
| Function F(x) = y |
Differential F'(x) = dy / dx |
| xn | n xn-1 |
| 1/x | -1/x2 |
| eax | a eax |
| Ln x | 1/x |
| Logax | 1/x Logae |
| sin ax | a cos ax |
| cos ax | -a sin ax |
| tan ax | a sec2 ax |
| cosec x | - cot x cosec x |
| sec x | tan x sec x |
| cot x | - cosec2 x |
| arcsin(x/a) | 1 / √ ( a2 - x2 ) |
| arccos(x/a) | -1 / √( a2 - x2 ) |
| arctan(x/a) | a / ( a2 + x2 ) |