derivative 1y^2-7y^4(y+9y^3)

解答

导数

1 y^{2} - 7 y^{4} (y + 9 y^{3})

2 y - 7 (63 y^{6} + 5 y^{4})

求解步骤

\frac{d}{d y} (1 \cdot y^{2} - 7 y^{4} (y + 9 y^{3}))

化简

1 \cdot y^{2} - 7 y^{4} (y + 9 y^{3}) : y^{2} - 7 y^{4} (y + 9 y^{3})

= \frac{d}{d y} (y^{2} - 7 y^{4} (y + 9 y^{3}))

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d y} (y^{2}) - \frac{d}{d y} (7 y^{4} (y + 9 y^{3}))

\frac{d}{d y} (y^{2}) = 2 y

\frac{d}{d y} (7 y^{4} (y + 9 y^{3})) = 7 (63 y^{6} + 5 y^{4})

= 2 y - 7 (63 y^{6} + 5 y^{4})

x \to 36 lim (\frac{x ^{2}}{9} - \frac{4}{x})

\int \frac{7}{4 + 7 x} d x

\frac{\partial}{\partial x} (3 x^{2} y + x sin (2 y))

y^{^{'}} + sin (t) y = - sin (t), y (0) = 7

\frac{\partial}{\partial x} (\frac{1}{4} x^{a} y^{1 - a})