derivative of (80sin(0.6x)/x+15)

解答

\frac{d}{d x} (\frac{80 sin ( 0.6 x )}{x} + 15)

\frac{80 ( 0.6 x cos ( 0.6 x ) - sin ( 0.6 x ) )}{x ^{2}}

求解步骤

\frac{d}{d x} (\frac{80 sin ( 0.6 x )}{x} + 15)

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{80 sin ( 0.6 x )}{x}) + \frac{d}{d x} (15)

\frac{d}{d x} (\frac{80 sin ( 0.6 x )}{x}) = \frac{80 ( 0.6 x cos ( 0.6 x ) - sin ( 0.6 x ) )}{x ^{2}}

\frac{d}{d x} (15) = 0

= \frac{80 ( 0.6 x cos ( 0.6 x ) - sin ( 0.6 x ) )}{x ^{2}} + 0

化简

= \frac{80 ( 0.6 x cos ( 0.6 x ) - sin ( 0.6 x ) )}{x ^{2}}

h \to 0 lim (\frac{7 ( a + h ) ^{2} - 7 a ^{2}}{h})

\int \frac{1}{sin ( 5 x ) cos ( 5 x )} d x

\int 8 e^{- t} d t

d er i v a t i v e - \frac{x ^{2}}{20} + 230 x - 74000

y^{^{''}} + 16 y = e^{3 x}