Wzory pochodnych i całek

Wzory pochodnych 1. (a) = 0 a-staªa 2. (xn ) = nxn−1 3. (ex ) = ex 4. (ln x) = 1 x 5. (sin x) = cos x 6. (cos x) = − sin x 7. (tg x) = 1 cos2 x 8. [h(...

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Wzory pochodnych 1.

(a)0 = 0

2.

(xn )0 = nxn−1

3.

(ex )0 = ex

4.

(ln x)0 =

5.

(sin x)0 = cos x

6.

(cos x)0 = − sin x

7.

(tg x)0 =

8.

[h(x)g(x)]0 = h0 (x)g(x) + h(x)g 0 (x) i0 h 0 0 (x) h(x) = h (x)g(x)−h(x)g g(x) g 2 (x)

9.

a-staªa

1 x

1 cos2 x

Wzory caªek 1 n+1 n+1 x

1.

R

xn dx =

2.

R

ex dx = ex + C

3.

R

1 x dx

4.

R

sin xdx = − cos x + C

5.

R

cos xdx = sin x + C

6.

R

1 cos2 x dx

7.

R

u(x)v 0 (x)dx = u(x)v(x) −

+C

= ln |x| + C

= tg x + C R

u0 (x)v(x)dx

1

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