derivative f(x)=x^3cos(x)

解答

导数

f (x) = x^{3} cos (x)

3 x^{2} cos (x) - x^{3} sin (x)

求解步骤

\frac{d}{d x} (x^{3} cos (x))

使用微分乘法定则:

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

f = x^{3}, g = cos (x)

= \frac{d}{d x} (x^{3}) cos (x) + \frac{d}{d x} (cos (x)) x^{3}

\frac{d}{d x} (x^{3}) = 3 x^{2}

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

= 3 x^{2} cos (x) + (- sin (x)) x^{3}

化简

= 3 x^{2} cos (x) - x^{3} sin (x)

\frac{d}{d x} ((sin (x))^{\frac{1}{3}})

l a pl a ce t r an s f or m 24 e^{- 7 t} - 5 e^{- 23 t}

\frac{d y}{d t} - 2 y = 4 - t

\frac{d}{d x} (- \frac{1}{4 ( 1 + x ) ^{\frac{3}{2}}})

\frac{\partial}{\partial y} (x yz + x y^{3} + y z^{3} + z x^{3})