PODSTAWOWE WZORY

(f ± g)

0

= f

0

± g

0

(f · g)

0

= f

0

· g + f · g

0

Ã

f

g

!

=

f

0

· g − f · g

0

g

2

(c)

0

= 0

(c · f )

0

= c · f

0

(x

r

)

0

= rx

r−1

(sin x)

0

= cos x

(cos x)

0

= − sin x

(tgx)

0

=

1

cos

2

x

(ctgx)

0

= −

1

sin

2

x

(a

x

)

0

= a

x

· ln a

(e

x

)

0

= e

x

(log

a

x)

0

=

1

x

·

1

ln a

(ln x)

0

=

1

x

(arcsin x)

0

=

1

√

1 − x

2

(arccos x)

0

= −

1

√

1 − x

2

(arctgx)

0

=

1

1 + x

2

(arcctgx)

0

= −

1

1 + x

2

(sinh x)

0

= cosh x

(cosh x)

0

= sinh x

1