Question

Calculati dirivata functiei:
a)f(x)=2x+1
b)f(x)=x^2-3x+4
c)f(x)=x^3
d)f(x)=1/x

Answer 1

$a)f(x) = 2x + 1$

$f'(x) = (2x + 1)'$

$f'(x) = (2x)' + 1'$

$f'(x) = 2x' + 0$

$f'(x) = 2 \times 1$

$f'(x) = 2$

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

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

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

$f'(x) = 2x - 3x' + 0$

$f'(x) = 2x - 3 \times 1$

$f'(x) = 2x - 3$

$c)f(x) = {x}^{3}$

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

$d)f(x) = \frac{1}{x}$

$f'(x) = ( \frac{1}{x} )' = \frac{ - x'}{ {x}^{2} } = - \frac{1}{ {x}^{2} } = - {x}^{ - 2}$