Question

Sa se calculeze derivatele functiilor f:D->R

a) f(x)= $x^{3} + 3x+ 1$
b) f(x)= $2x - x^{4}$
c) f(x)= $x+ 2 \sqrt{x}$
d) f(x)= $x^{3} + sin x + cos x$

Va rog ajutati-ma

Answer 1

a) 
f ' (x) = $3x^{2} + 3 = 3( x^{2} +1)$

b)
f ' (x) = $2 - 4 x^{3} = 2(1-2 x^{3})$

c)
f ' (x) = $1 + \frac{1}{ \sqrt{x} }$
(2√x ) ' = $2'* \sqrt{x} +2*( \sqrt{x} )'=0* \sqrt{x} +2*(1/2 \sqrt{x} )=0+1/ \sqrt{x} = 1 / \sqrt{x}$

d)
f ' (x) = $3 x^{2} -cosx-sinx$