Question

Ache as derivada
1)y=4³x²
2)y=x⁵-2x³+x
3)y=x²/x²+4
4)y=3/2x-1

Answer 1

#1 TEOREMA, DERIVA DE UMA FUNÇÃO DO TIPO "aⁿ"

temos que:

f(x) = aⁿ

$f'(x) = n. {a}^{n - 1}$

1)

$\frac{d}{dx} ( {4}^{3} . {x}^{2} ) = {4}^{3} .2x$

2)

f(x) = x⁵ - 2x³ + x

$f'(x) = {5x}^{4} - 2.3x ^{2} + 1 \\ f'(x) = {5x}^{4} - 6x ^{2} + 1$

3)

f(x) = x² / x² + 4

$f'(x) = \frac{(x^{2} )'.( {x}^{2} + 4) - ( {x}^{2} ).( {x}^{2} + 4)'}{( {x}^{2} + 4)^{2} }$

$f'(x) = \frac{(2x).( {x}^{2} + 4) - ( {x}^{2} ).(2x) }{( {x}^{2} + 4) ^{2} }$

$f'(x) = \frac{(2x).( {x}^{2} + 4 - {x}^{2} ) }{( {x}^{2} + 4) ^{2} }$

$f'(x) = \frac{8x}{( {x}^{2} + 4)^{2} }$