Calcolo differenziale, teoremi derivate

DERIVATA SENODEL4

line(a) l'senosenxSen' Sery 1m-= ==✗ O X✗→ -0 o- senlxothlievi )(Sen' ) sento11insentoseniXo -- == hhXo o✗ -Xo✗→ - sentifyugcoshn-1-tcosxo.limsenhh.ioCashlui sentocostosento sento+ . --= = . hh o→fycosnhz-1-I.ph/ b)hCashlin -1 Sento COSXOSento costocosto ++= = . =. .hah o→ → T (OSXSen' ✗ =HEIRCOSENODERIVATA5. DELCOS' Senx✗ -=REGOLETEOREMA PER DERIVATEDICALCOLOILDERIVATA DELLA SOMMA1. ( " f')Lf ( Bg ABER( (=L )Bg ) '××+ +xDIM ÈÈHf+pg)(×-É PIÈ " f-× '' )(a) Bg (✗ ' Xo✗ ++ >= X XoX Xo✗ Xo ---REGOLA DEL PRODOTTOLEIBNITZ DERIVATADI2. formula consideraquesta funzioneanche valori dellaf. flxlg i( f-'g) '( glx)G) ' ( )) + × nelx punto= .DIM )f-f-funghi ( flx /f- (01940( ) )( )( ( gliog)f- f- (g) ) gcx( )) glx )Xo)() ✗Xo + -xo- -× -- == XoX✗ XoXo ✗-- -f- f- -94f-)( »( "

✗)) 9 ✗Xo g(× →) ( °) derivabile- poiché gl'× ✗ o in= + ,. . liXo✗ X Xo Xo ' continua- e- f-t' )glioHo Ho () s' )) Xo+ --> DERIVATA RAPPORTODEL3. ( " f') f-§ Igilx( )( glx) )) ( ✗× 91×1=10x -- se= ≥)glxFUNZIONE COMPOSTADERIVAZIONE4. ( " f-f) )/ fa( '' () ) )g×go ×= . divisomoltiplicato @ perf- f-h( ( )) ×✗+ -DIM ↓)(( ) /f) f) )(( / ))( / -91fth ) / tutti1-fcxth) f( 1))) f-( »)×✗ 99 h×+ ggo g. ) (- ✗ ✗- + -= == f- flxh hh )(h )✗ + -f-f- th f-Poiche h( )(Sia derivabile) anche' ' quindi✗ y' e Zin✗ ✗2- continua× 0pere↳ - ee →in== ,)(f- )SHHth )( 94)9 ) 919 )✗ luifu fa )- / )'- ( )g. gy == =f- f-" 2- y)th → y( z° ( ) -✗ ×-" f-9 / ) 'f- ( )' ( ) ×g= × .FUNZIONEDERIVATA INVERSA5. f-1)( /f- ((g) f-' '' =/)( ose y= 'f / )f- '

lui )^/ f-4tangenteretta a)Glf " y ✗a - (f)4tangente aretta"""-)(coefficiente (flx4ft) )Il della tangentedelladi'tangente ) il reciproco quelloa × e serain y× c ,,=/ () ))/ (f- flxl4 'f-' ) ( )a × yzin yy =,,