|
(a + b)^2
|
a^2 + b^2 + 2ab
|
f (x) = arcsin x :
|
f '(x) = 1 / √(1-x^2) |
f (x) = u(x) * v(x) :
|
f '(x) = u'(x) * v(x) + u(x) * v'(x) |
f (x) = x :
|
f '(x) = 1 |
f (x) = sin x :
|
f '(x) = cos x |
f (x) = arctg x :
|
f '(x) = -1 / √(1-x^2) |
f (x) = k :
|
f '(x) = 0 |
|
(a + b)^2
|
a^2 + b^2 + 2ab
|
f (x) = u(x) + v(x) :
|
f '(x) = u'(x) + v'(x) |
f (x) = ax + b :
|
f '(x) = a |
f (x) = k * u(x) :
|
f '(x) = k * u'(x) |
f (x) = u(x) / v(x) :
|
( u'(x) * v(x) - u(x) * v'(x) ) / v^2(x) |
f (x) = x^n :
|
f '(x) = n * x^(n-1) |
f (x) = e^x :
|
f (x) = e^x |
|
(a + b)^2
|
a^2 + b^2 + 2ab
|
f (x) = cos x :
|
f '(x) = -sin x |
f (x) = tg x :
|
f '(x) = 1 / cos^2 x = 1 + tg^2 x |
f (x) = a^x :
|
f '(x) = a^x * ln a |
f (x) = ln x :
|
f '(x) = 1/x |
f (x) = log_a x :
|
f '(x) = ( 1 / x )log_a e |
f (x) = cotg x :
|
f '(x) = -1 / sin^2 x = -( 1 + cotg^2 x) |
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