展开 (y^2+5x^3) derivative of+xy

解答

展开

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

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

求解步骤

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

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

使用分配律:

a (b + c) = ab + a c

a = \frac{d}{d x} (x y), b = y^{2}, c = 5 x^{3}

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

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

e x p an d 5 (2 e^{x} + \frac{1}{4} e^{4 x}) + C

e x p an d (1 + tan (x)) \cdot (1 + co tan (x))

s im pl i f y (x - 3) (x + 12 + \frac{29}{x - 3})

e x p an d \frac{5 ( 2 - x ^{2} ) ^{2}}{2}

e x p an d 7 x - 1 \cdot (x - 1)^{7}