derivative y=e^{8x}cos(11x)

解答

导数

y = e^{8 x} cos (11 x)

8 e^{8 x} cos (11 x) - 11 e^{8 x} sin (11 x)

求解步骤

\frac{d}{d x} (e^{8 x} cos (11 x))

使用微分乘法定则:

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

f = e^{8 x}, g = cos (11 x)

= \frac{d}{d x} (e^{8 x}) cos (11 x) + \frac{d}{d x} (cos (11 x)) e^{8 x}

\frac{d}{d x} (e^{8 x}) = e^{8 x} \cdot 8

\frac{d}{d x} (cos (11 x)) = - sin (11 x) \cdot 11

= e^{8 x} \cdot 8 cos (11 x) + (- sin (11 x) \cdot 11) e^{8 x}

化简

= 8 e^{8 x} cos (11 x) - 11 e^{8 x} sin (11 x)

\int \frac{1}{( 5 x - 3 ) ( 3 - 4 x )} d x

d er i v a t i v e ln (2 - x)

\int x^{2} (7 - x^{3})^{\frac{2}{3}} d x

\frac{d}{d x} (tan (x^{2} - 4 x))

x \to - \infty lim (x^{3} - 5 x^{2})