Question

Sa se calculeze derivatele funcțiilor scriindu-se de fiecare data si formulele utilizate :
a) f:IR -> IR , f(x) = -8x²+x-12
b) f:IR -> IR , f(x) = 3x⁵+ 7 la x
c) f:IR -> IR , f(x) = 2 e la x + 2 la x - 4 la x
d) f:IR\{0} -> IR , f(x) = 3x la a 7 + 1 supra x la a doua - 1 supra x la a patra.
e) f:IR \ { -1 } -> IR , f(x) = x - 3 supra x+1
f) f:IR -> IR , f(x) = - X +3 supra x la a doua + 1
g) f:IR -> IR , f(x) = ( X la a doua + 3x-2 ) e la x
h) f: ( 0 , plus infinit ) -> IR , f(x) = xIn7+2Inx
i) f: ( 0 , plus infinit ) -> IR , f(x) = ( X la a doua + 2 ) Inx
j) f:IR -> IR , f(x) = -3sinx + 2cosx
k) f:IR -> IR , f( x) = ( 3x+4 ) cos x
l) f : ( -1 , 1 ) -> IR , f(x) = 4 arcsin + 3 arccosx
m) f: ( -1 , 1 ) -> IR , f(x) = ( 2x-3 ) arcsinx
n) f:IR -> IR , f(x) = 2cosx-3 supra sinx+2
o) f:IR -> IR , f(x) = 6 arcctgx - arctgx
p) f: IR ( 0 , plus infinit ) -> IR , f(x) = 2 radical din x + ⁴radical din x - 1 supra radical din x plus 1 supra 5 radical din x ³.
AJUTOR !!!! AM MARE NEVOIE DE ACEST EXERCIȚIU.​

Answer 1

Răspuns:

Explicație pas cu pas:

a) f:R->R, f(x) =-8x²+x-12

f'(x)=-16x+1

b) f:IR -> IR , f(x) = 3x⁵+ 7 ^x

f'(x)=15x+7^x ·ln7

c) f:IR -> IR , f(x) = 2 e ^ x + 2 ^x - 4 ^x

f'(x)=2e^x+2^x×ln2-4^x×ln4

d) f:IR\{0} -> IR , f(x) = 3x ^7 + 1 /x ² - 1 / x^4

f'(x)=3x^7×ln3×7x^6+1/x^4·2x-1/x^8×4x=21x^13×ln3+2/x³-4/x^7

j) f:IR -> IR , f(x) = -3sinx + 2cosx

f'(x)=-3cosx-2sinx

h) f: ( 0 , plus infinit ) -> IR , f(x) = xIn7+2Inx

f'(x)=ln7+2/x

k) f:IR -> IR , f( x) = ( 3x+4 ) cos x

f'(x)=3 cosx-(3x+4) sin x

postaeza restul inca o data, merci