derivative y=1.45e^{59.9t}sin(201t)

解答

导数

y = 1.45 e^{59.9 t} sin (201 t)

1.45 (e^{59.9 t} \cdot 59.9 sin (201 t) + cos (201 t) \cdot 201 e^{59.9 t})

求解步骤

\frac{d}{d t} (1.45 e^{59.9 t} sin (201 t))

将常数提出:

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

= 1.45 \frac{d}{d t} (e^{59.9 t} sin (201 t))

使用微分乘法定则:

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

f = e^{59.9 t}, g = sin (201 t)

= 1.45 (\frac{d}{d t} (e^{59.9 t}) sin (201 t) + \frac{d}{d t} (sin (201 t)) e^{59.9 t})

\frac{d}{d t} (e^{59.9 t}) = e^{59.9 t} \cdot 59.9

\frac{d}{d t} (sin (201 t)) = cos (201 t) \cdot 201

= 1.45 (e^{59.9 t} \cdot 59.9 sin (201 t) + cos (201 t) \cdot 201 e^{59.9 t})

\int_{2}^{6} t^{4} ln (3 t) d t

a re a y = \frac{3}{x} + 2 x^{3}, 2 \leq x \leq 3

t an g e n t f (x) = - 2 x^{3}, (1, - 2)

\frac{d}{d x} (x (x + 12))

\frac{\partial}{\partial x} (3 z cos (4 x y) + x - 7 y)