Exercitiul 1:
Folosim tabelul de derivare
a) 2x-5
c) [tex]3-6x^{5}[/tex]
e) [tex]2^{x}*ln2 + 3^{x}*ln3 - \frac{1}{3\sqrt[3]{x^{2} } }[/tex]
g) [tex](x^{2} - 6x + 9)'[/tex] = 2x-6
Exercitiul 2:
Folosim formula (u*v)' = u'*v + u*v'
a) [tex](x*e^{x})' = x'* e^{x} + x*(e^{x})' = e^{x} + x*e^{x} = e^{x}(x+1)[/tex]
d) [tex]((3x-1)*\sqrt{x})' = (3x-1)'*\sqrt{x} + (3x-1)(\sqrt{x})' = 3\sqrt{x} + \frac{3x-1}{2\sqrt{x} }[/tex]
g) [tex](2x*sinx)' = (2x)'*sinx + 2x *sin'x = 2*sinx + 2x*cosx[/tex]
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)
