d/(d{y)}(({z}(x))({x}{y}+sin({x}{y})+{x}))

解答

\frac{d}{d y} ((z (x)) (x y + sin (x y) + x))

z (x) (x + cos (x y) x + \frac{d}{d y} (x))

求解步骤

\frac{d}{d y} ((z (x)) (x y + sin (x y) + x))

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= z (x) \frac{d}{d y} (x y + sin (x y) + x)

使用微分加减法定则:

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

= z (x) (\frac{d}{d y} (x y) + \frac{d}{d y} (sin (x y)) + \frac{d}{d y} (x))

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

\frac{d}{d y} (sin (x y)) = cos (x y) x

= z (x) (x + cos (x y) x + \frac{d}{d y} (x))

s im pl i f y \frac{( p + q + p - q ) ^{2}}{2 q}

e x p an d (3 x^{4} + 6 x^{2} - 2)^{5}

e x p an d \frac{( x + 1 ) ( 6 x - 7 )}{( x + 3 ) ( x - 3 ) ( 3 x + 2 )}

e x p an d \frac{( x - 2 ) ( x + 3 )}{x + 4}

e x p an d \frac{1}{( 3 n + 1 ) ^{15}}