derivative of 2xy

解答

\frac{d}{d x} (2 \cdot x \cdot y)

2 (y + x \frac{d y}{d x})

求解步骤

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

将常数提出:

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

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

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = y

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

\frac{d x}{d x} = 1

= 2 (1 \cdot y + \frac{d y}{d x} x)

化简

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

\int \frac{e ^{x}}{2} d x

\frac{d}{d t} (a cos (2 t) + b sin (2 t))

\int sin^{2} (x - y) d y

t an g e n t y = x^{2} + 2 x + 10, at x = 6

\frac{d y}{d x} = 2 y + x^{2} e^{2 x} + 5