derivative of e^x*cos(y)

解答

\frac{d}{d x} (e^{x} \cdot cos (y))

e^{x} cos (y) - e^{x} sin (y) \frac{d y}{d x}

求解步骤

\frac{d}{d x} (e^{x} cos (y))

使用微分乘法定则:

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

f = e^{x}, g = cos (y)

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

\frac{d}{d x} (e^{x}) = e^{x}

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

= e^{x} cos (y) + (- sin (y) \frac{d y}{d x}) e^{x}

化简

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

\int y e^{y} d y

x \to 0 lim (\frac{x ^{2} + 1}{x})

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

\frac{d}{d x} (1 - e^{- 0.1 x})

s l o p e (4 x + 4 y)^{3} = 64 x^{3} + 64 y^{3} (- 1.1)