derivative of (sin(3x)/(cos(2x)))

解答

\frac{d}{d x} (\frac{sin ( 3 x )}{cos ( 2 x )})

cos (3 x) \cdot 3 sec (2 x) + sec (2 x) tan (2 x) \cdot 2 sin (3 x)

求解步骤

\frac{d}{d x} (\frac{sin ( 3 x )}{cos ( 2 x )})

化简

\frac{sin ( 3 x )}{cos ( 2 x )} : sin (3 x) sec (2 x)

= \frac{d}{d x} (sin (3 x) sec (2 x))

使用微分乘法定则:

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

f = sin (3 x), g = sec (2 x)

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

\frac{d}{d x} (sin (3 x)) = cos (3 x) \cdot 3

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

= cos (3 x) \cdot 3 sec (2 x) + sec (2 x) tan (2 x) \cdot 2 sin (3 x)

d er i v a t i v e arcsin (\frac{x}{9})

t an g e n t f (x) = \frac{e ^{x}}{x}, e, at x = 1

\int (9 x - 6)^{2} d x

d er i v a t i v e - x e^{x}

a re a y^{2} = x + 4, y^{2} = 2 - x