derivative e^{7x}cos(10x)

解答

导数

e^{7 x} cos (10 x)

7 e^{7 x} cos (10 x) - 10 e^{7 x} sin (10 x)

求解步骤

\frac{d}{d x} (e^{7 x} cos (10 x))

使用微分乘法定则:

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

f = e^{7 x}, g = cos (10 x)

= \frac{d}{d x} (e^{7 x}) cos (10 x) + \frac{d}{d x} (cos (10 x)) e^{7 x}

\frac{d}{d x} (e^{7 x}) = e^{7 x} \cdot 7

\frac{d}{d x} (cos (10 x)) = - sin (10 x) \cdot 10

= e^{7 x} \cdot 7 cos (10 x) + (- sin (10 x) \cdot 10) e^{7 x}

化简

= 7 e^{7 x} cos (10 x) - 10 e^{7 x} sin (10 x)

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

d er i v a t i v e y = - 2 x^{2} + 24

\int_{0}^{1} e^{x} (e^{x} - 1) d x

l a pl a ce t r an s f or m 30 t^{2}

x \to \infty lim (- ln (x))