derivative of x^3cos(x^3)

解答

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

3 x^{2} cos (x^{3}) - 3 x^{5} sin (x^{3})

求解步骤

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

使用微分乘法定则:

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

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

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

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

\frac{d}{d x} (cos (x^{3})) = - sin (x^{3}) \cdot 3 x^{2}

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

化简

3 x^{2} cos (x^{3}) + (- sin (x^{3}) \cdot 3 x^{2}) x^{3} : 3 x^{2} cos (x^{3}) - 3 x^{5} sin (x^{3})

= 3 x^{2} cos (x^{3}) - 3 x^{5} sin (x^{3})

\frac{d y}{d x} = 8 x - 4 x y

\frac{d}{d x} (6 x^{2})

\int 9 (sec (x))^{2} d x

7 y^{^{''}} + 27 y = 0, y (0) = 6, y^{^{'}} (0) = 5

\int - 5 x^{- 6} d x