derivative x^6cos(x)

解答

导数

x^{6} cos (x)

6 x^{5} cos (x) - x^{6} sin (x)

求解步骤

\frac{d}{d x} (x^{6} cos (x))

使用微分乘法定则:

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

f = x^{6}, g = cos (x)

= \frac{d}{d x} (x^{6}) cos (x) + \frac{d}{d x} (cos (x)) x^{6}

\frac{d}{d x} (x^{6}) = 6 x^{5}

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

= 6 x^{5} cos (x) + (- sin (x)) x^{6}

化简

= 6 x^{5} cos (x) - x^{6} sin (x)

d er i v a t i v e y (s) = \frac{1}{s + k e ^{s}}

n = 1 \sum \infty arcsin (n)

y^{^{''}} + 4 y^{^{'}} - 5 y = e^{3 x}

\frac{d}{d x} (\frac{x ^{9}}{45})

a re a y = 6 x, y = 6 x^{2}