derivative f(t)=2tsin(pit)

解答

导数

f (t) = 2 t sin (π t)

2 (sin (π t) + π t cos (π t))

求解步骤

\frac{d}{d t} (2 t sin (π t))

将常数提出:

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

= 2 \frac{d}{d t} (t sin (π t))

使用微分乘法定则:

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

f = t, g = sin (π t)

= 2 (\frac{d t}{d t} sin (π t) + \frac{d}{d t} (sin (π t)) t)

\frac{d t}{d t} = 1

\frac{d}{d t} (sin (π t)) = cos (π t) π

= 2 (1 \cdot sin (π t) + cos (π t) π t)

化简

= 2 (sin (π t) + π t cos (π t))

\int \frac{4 x ^{2} + 21 x + 54}{x ^{2} + 6 x + 13} d x

x \to 8 lim (6 x^{2} - 9 x + 1)

t a y l or (\frac{3}{2})^{x}

y^{^{''}} - 4 y^{^{'}} + 2 y = 0, y (0) = 0, y^{^{'}} (0) = 1

\frac{\partial}{\partial y} (4 e^{x} ln (y))