expandir x^7(a(dy)/(dx)+bx^5y^5)

Solução

expandir

x^{7} (a \frac{d y}{d x} + b x^{5} y^{5})

a x^{7} \frac{d y}{d x} + b x^{12} y^{5}

Passos da solução

x^{7} (a \frac{d y}{d x} + b x^{5} y^{5})

Colocar os parênteses utilizando:

a (b + c) = ab + a c

a = x^{7}, b = a \frac{d y}{d x}, c = b x^{5} y^{5}

= x^{7} a \frac{d y}{d x} + x^{7} b x^{5} y^{5}

= a x^{7} \frac{d y}{d x} + b x^{7} x^{5} y^{5}

b x^{7} x^{5} y^{5} = b x^{12} y^{5}

= a x^{7} \frac{d y}{d x} + b x^{12} y^{5}

e x p an d x^{x^{x}} (x^{x} ln (x) (ln (x) + 1) + x^{x - 1})

e x p an d (13, - 3, 4) x (8, - 4, 3)

e x p an d (a + b x + c x^{2} + d x^{3} + e x^{4})^{2}

e x p an d \frac{( ( a \cdot ( 1 + g ) ^{n} ) \cdot ( 1 - 0.6 a ) ) - 20}{20}

e x p an d \frac{e ^{- 4 s} ( \frac{1}{s ^{2}} + \frac{3}{s} ) - 5}{s ^{2} + 5 s + 8}