Dada a função f(x)=(1−2xx2+x)4 , o valor da derivada de f (x) será

f′(x)=4(1−2x)5(x2+x)3(1+2x−2x2)

f′(x)=(1−2x)5(x2+x)3(−2x2+2x+1)

f′(x)=(1−2x)4(4x2+4x)3(1+2x−2x2)

f′(x)=4(1−2x)5(x2+x)3(1−2x−2x2)

Dada a função f(x)=(1−2xx2+x)4 , o valor da derivada de f...

Q1854775

Dada a função $f (x) = (\frac{x ^{2} + x}{1 - 2 x})^{^{^{4}}}$ , o valor da derivada de f (x) será

$f^{'} (x) = \frac{( x ^{2} + x ) ^{^{3}} ( - 2 x ^{2} + 2 x + 1 )}{( 1 - 2 x ) ^{5}}$

$f^{'} (x) = 4 \frac{( x ^{2} + x ) ^{^{3}}}{( 1 - 2 x ) ^{5}} (1 + 2 x - 2 x^{2})$

$f^{'} (x) = \frac{( 4 x ^{2} + 4 x ) ^{^{3}}}{( 1 - 2 x ) ^{4}} (1 + 2 x - 2 x^{2})$

$f^{'} (x) = 4 \frac{( x ^{2} + x ) ^{^{3}}}{( 1 - 2 x ) ^{5}} (1 - 2 x - 2 x^{2})$

$f^{'} (x) = - 4 \frac{( 2 x + 1 ) ^{3}}{2}$