(\partial)/(\partial x)(tan(2x)sin(2x))

解答

\frac{\partial}{\partial x} (tan (2 x) sin (2 x))

2 sin (2 x) + 2 sec (2 x) tan (2 x)

求解步骤

\frac{\partial}{\partial x} (tan (2 x) sin (2 x))

使用微分乘法定则:

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

f = tan (2 x), g = sin (2 x)

= \frac{\partial}{\partial x} (tan (2 x)) sin (2 x) + \frac{\partial}{\partial x} (sin (2 x)) tan (2 x)

\frac{\partial}{\partial x} (tan (2 x)) = sec^{2} (2 x) \cdot 2

\frac{\partial}{\partial x} (sin (2 x)) = cos (2 x) \cdot 2

= sec^{2} (2 x) \cdot 2 sin (2 x) + cos (2 x) \cdot 2 tan (2 x)

化简

sec^{2} (2 x) \cdot 2 sin (2 x) + cos (2 x) \cdot 2 tan (2 x) : 2 sin (2 x) + 2 sec (2 x) tan (2 x)

= 2 sin (2 x) + 2 sec (2 x) tan (2 x)

d er i v a t i v e f (x) = 4 x^{2} - 5 x

\frac{\partial}{\partial z} (cos (x z))

n = 1 \sum \infty \frac{n}{2 n ^{3} + 1}

t an g e n t \frac{2}{x}, at x = \frac{1}{9}

\frac{d}{d x} (x (2))