d/(dy)(e^ycos(y))

解答

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

e^{y} cos (y) - e^{y} sin (y)

求解步骤

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

使用微分乘法定则:

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

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

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

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

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

= e^{y} cos (y) + (- sin (y)) e^{y}

化简

= e^{y} cos (y) - e^{y} sin (y)

\int tan^{2} (x) sec^{6} (x) d x

\int x (x^{2} + 1)^{100} d x

l o n g d i v i s i o n \frac{x ^{2} - 10 x + 65}{x - 8}

n = 0 \sum \infty \frac{1}{( 2 n - 1 ) ^{2}}

x \to 5 lim (\frac{sin ( 5 π )}{3})