Derivaatat

Question 1

Rationaali, esim [1/x^3]

Answer 1

[x^3/1] -> [-3x^-4] -> -3/x^4

Question 2

Radikaali, esim [cube root x 5]

Answer 2

[x^5/3] -> [5/3x^2/3] -> [5x^2/3 / 3] -> 5 cube root of 2 / 3

Question 3

Trigonometriset:

Answer 3

[sin u] = cos u x u’

[cos u] = -sin u x u’

Question 4

Luonnollinen log:

Answer 4

[ln u] = u’/u

Question 5

10 kantainen log:

Answer 5

[log a u ] = u’/u ln a

Question 6

Exponentit:

Answer 6

[e^u] = e^u x u'
[a^u] = a^u x u' x ln a

Question 7

Kertolasku:

Answer 7

[u x v] = u’ x v + u x v’

Question 8

Jakolasku:

Answer 8

[u/v] = v x u’ - u x v’ / v^2

Question 9

Yhteisfunktio:

Answer 9

[ f [ g (x) ] ] = f’ [g(x)] x g’ (x)

Question 10

Kun laskussa on sekä x ja y:

Answer 10

Esim: x^4 + y^4 = 12

4x^3 + 4y^3 x dy/dx