Question

Hi

Calcule a primeira derivada :
a)[tex] f(x) = 7[\tex]
b)[tex] f(x) = 4x[\tex]
c)[tex] f(x) = 2 \sqrt{2}x + 4\sqrt{3}[\tex]
d)[tex] f(x) =x¹⁰[\tex]
e)[tex]f(x) = 4x³ + 2x² + 2x + 5[\tex]​

Answer 1

Explicação passo-a-passo:

a)

$\sf f(x)=7$

A derivada de uma constante é zero

$\sf f'(x)=0$

b)

$\sf f(x)=4x$

$\sf f'(x)=1\cdot4x^{1-1}$

$\sf f'(x)=4$

c)

$\sf f(x)=2\sqrt{2}x+4\sqrt{3}$

$\sf f'(x)=1\cdot2\sqrt{2}x^{1-1}+0$

$\sf f'(x)=2\sqrt{2}$

d)

$\sf f(x)=x^{10}$

$\sf f'(x)=10x^{10-1}$

$\sf f'(x)=10x^9$

e)

$\sf f(x)=4x^3+2x^2+2x+5$

$\sf f'(x)=3\cdot4x^{3-1}+2\cdot2x^{2-1}+1\cdot2x^{1-1}+0$

$\sf f'(x)=12x^2+4x+2$