derivative sin(x)*cos(x)

解答

导数

sin (x) \cdot cos (x)

cos (2 x)

求解步骤

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

使用微分乘法定则:

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

f = sin (x), g = cos (x)

= \frac{d}{d x} (sin (x)) cos (x) + \frac{d}{d x} (cos (x)) sin (x)

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

\frac{d}{d x} (cos (x)) = - sin (x)

= cos (x) cos (x) + (- sin (x)) sin (x)

化简

cos (x) cos (x) + (- sin (x)) sin (x) : cos (2 x)

= cos (2 x)

d er i v a t i v e (1.01)^{x} + 0.3 3^{x}

\frac{d}{d r} (\frac{2 k}{r} + 2 π r^{2})

(y^{2} + 9) d x - \frac{1}{( 2 x + 1 ) ^{2}} d y = 0

\int 5 x 1 - x^{2} d x

\frac{d}{d x} (\frac{3 x + 2}{x + 1})