Question

Va rog frumos, puteți rezolva de la 1, a, c, e, g, 2,a,d,g,j dau 40 puncte ​

Answer 1

Exercitiul 1:

Folosim tabelul de derivare

a) 2x-5

c) $3-6x^{5}$

e) $2^{x}*ln2 + 3^{x}*ln3 - \frac{1}{3\sqrt[3]{x^{2} } }$

g) $(x^{2} - 6x + 9)'$ = 2x-6

Exercitiul 2:

Folosim formula (u*v)' = u'*v + u*v'

a) $(x*e^{x})' = x'* e^{x} + x*(e^{x})' = e^{x} + x*e^{x} = e^{x}(x+1)$

d)  $((3x-1)*\sqrt{x})' = (3x-1)'*\sqrt{x} + (3x-1)(\sqrt{x})' = 3\sqrt{x} + \frac{3x-1}{2\sqrt{x} }$

g) $(2x*sinx)' = (2x)'*sinx + 2x *sin'x = 2*sinx + 2x*cosx$

j) ((x+1)(sinx-5cosx))' =(x+1)' (sinx-5cosx) + (x+1)(sinx-5cosx)'

Calculam separat :

(x+1)'=1

(sinx-5cosx)' = cosx +5sinx

Deci derivata noastra = (sinx-5cosx) + (x+1)(cosx +5sinx)