d/(d{y)}(({f}(y))({y}+cos({y})))

解答

\frac{d}{d y} ((f (y)) (y + cos (y)))

f (y) (1 - sin (y))

求解步骤

\frac{d}{d y} ((f (y)) (y + cos (y)))

将常数提出:

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

= f (y) \frac{d}{d y} (y + cos (y))

使用微分加减法定则:

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

= f (y) (\frac{d}{d y} (y) + \frac{d}{d y} (cos (y)))

\frac{d}{d y} (y) = 1

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

= f (y) (1 - sin (y))

s im pl i f y 7 (7 + x 14)

e x p an d 2 [(x + 3) (x + 2)]

e x p an d \frac{5 x ^{2} - 9 x + 19}{( x - 4 ) ( x ^{2} + 5 )}

e x p an d (b c + d e)^{6}

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