semplificare ((x+Δx)^3-x^3)/(Δx)

Soluzione

semplificare

\frac{( x + Δ x ) ^{3} - x ^{3}}{Δ x}

Δ^{2} x^{2} + 3Δ x^{2} + 3 x^{2}

Fasi della soluzione

\frac{( x + Δ x ) ^{3} - x ^{3}}{Δ x}

Fattorizza

(x + Δ x)^{3} - x^{3} : Δ x ((x + Δ x)^{2} + x (x + Δ x) + x^{2})

= \frac{Δ x ( ( x + Δ x ) ^{2} + x ( x + Δ x ) + x ^{2} )}{Δ x}

Cancellare

\frac{Δ x ( ( x + Δ x ) ^{2} + x ( x + Δ x ) + x ^{2} )}{Δ x} : (x + Δ x)^{2} + x (x + Δ x) + x^{2}

= (x + Δ x)^{2} + x (x + Δ x) + x^{2}

(x + Δ x)^{2} : x^{2} + 2Δ x^{2} + Δ^{2} x^{2}

= x^{2} + 2Δ x^{2} + Δ^{2} x^{2} + x (x + Δ x) + x^{2}

Espandi

x (x + Δ x) : x^{2} + Δ x^{2}

= x^{2} + 2Δ x^{2} + Δ^{2} x^{2} + x^{2} + Δ x^{2} + x^{2}

Semplifica

x^{2} + 2Δ x^{2} + Δ^{2} x^{2} + x^{2} + Δ x^{2} + x^{2} : Δ^{2} x^{2} + 3Δ x^{2} + 3 x^{2}

= Δ^{2} x^{2} + 3Δ x^{2} + 3 x^{2}

s im pl i f y (\frac{1}{2} - 3)^{6}

s im pl i f y 4 (2 x^{2} y - 4 x) + 3 x - 2 x (5 x y - 4) + 12

s im pl i f y \frac{2 7 ^{4}}{9 ^{5}}

s im pl i f y \frac{6 a + 10}{6 a - 9 ab + 10 - 15 b}

f a c t or 36 c d - 11 c a^{2}