Question

Determinar a derivada das seguintes funções:
a) f(x)= 3x + 2
b) f(x)= 1 - 4x²
c) f(x)= $1 \\ x+2$
d) f(x)= 2x² - x - 1

Answer 1

a )

$(f+g)'=f'+g'$

$f(x)=3x^1+2\\f'(x)=1*3x^{0}+0\\f'(x)=3$

b )

$(f-g)'=f'-g'$

$f(x)=1-4x^2\\f'(x)=0-2*4x^{2-1}\\f'(x)=8x$

c )

$f(g(x))'=f'(g(x))*g'(x)$

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

d )

$f(x)=2x^2-x-1\\f'(x)=2*2x^{2-1}-1*x^{0}+0\\f'(x)=4x-1$