Türev alma kuralları

TÜREV ALMA KURALLARI

1. f(x)

c ise f (x)

cot u(x) ise

14. f(x)

0

f (x) 2. f(x)

xn ise f (x)

n xn

u (x) 1

1

u (x)

f (x) 3. f(x)

c u(x) ise f (x)

4. f(x)

u(x)

c u (x)

v(x) ise f (x)

v (x) 15.

5. f(x)

f (x)

6. f(x)

v(t)

x

u(t)

u (x) v(x)

dy dx

v (x) u(x)

u (x) v(x)

dy dt dx dt

g(x) ise f (x)

f g(x)

n

g(x)

m

n

g(x)

n

g(x)

u (x) eu(x)

18. f(x)

au(x) ise f (x)

u (x) au(x) ln a

19. f(x)

lnu(x) ise f (x)

u (x) u(x)

loga u(x) ise

u (x) loga e , f (x) u(x)

f (x)

u (x) u(x).lna

ise 21. f(x)

y

u(x)

v(x)

ise

n m

lny 11. f(x)

sinu(x) ise f (x)

12. f(x)

cos u(x) ise f (x)

u (x) cos u(x)

u (x) sinu(x)

tanu(x) ise

ln u(x)

v(x)

v(x) lnu(x)

y y

v (x) lnu(x)

y

y. v (x) lnu(x)

y

u(x)

v(x)

u (x) v(x) u(x)

u (x) v(x) u(x) u (x) v(x) u(x)

. v (x) lnu(x)

tan2 u(x)

u (x) cos2 u(x)

f (x)  u(x)  sec 2 u(x)

lisanhoca

u (x) 1

1 f (x)

eu(x) ise f (x)

n 1

m g (x) n

(y)

17. f(x)

20. (a1) için f(x)

g (x) n

f (x)

1

f 1(y) ise f

x

g(x)

g(x) ise f (x)

10. (n>m) için f(x)

g (x)

g (x) 2

n

f(x)

v (t) u (t)

2

8. f(x)

f (x)

dy dt dt dx

v (x) u(x)

f g (x) ise h (x)

f (x)

f(x) ise

u(x) ise v(x)

7. h(x)

13. f(x)

y

u(x) v(x) ise

v(x)

9. f(x)

u (x) cosec 2 u(x)

y

16. y

f (x)

sin2 u(x)

f (x)

u (x)

cot 2 u(x)

22. F(x,y)

0 ise y

dy dx

Fx Fy