derivative y^2x+5xy^3+10y^2+8xy

解答

导数

y^{2} x + 5 x y^{3} + 10 y^{2} + 8 x y

2 x y + 15 x y^{2} + 20 y + 8 x

求解步骤

\frac{d}{d y} (y^{2} x + 5 x y^{3} + 10 y^{2} + 8 x y)

将

x

视为常数

使用微分加减法定则:

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

= \frac{d}{d y} (y^{2} x) + \frac{d}{d y} (5 x y^{3}) + \frac{d}{d y} (10 y^{2}) + \frac{d}{d y} (8 x y)

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

\frac{d}{d y} (5 x y^{3}) = 15 x y^{2}

\frac{d}{d y} (10 y^{2}) = 20 y

\frac{d}{d y} (8 x y) = 8 x

= 2 x y + 15 x y^{2} + 20 y + 8 x

\frac{d}{d a} (\frac{( cos ( a ) )}{( 1 - sin ( a ) )})

d er i v a t i v e y = \frac{1}{( x ^{2} + 4 )}

\frac{d}{d x} (x^{3} sin (y^{3}))

d er i v a t i v e y = sin (e^{2} x)

d er i v a t i v e x^{x} - 2^{s} in x