derivative x^2sin(5x)

解答

导数

x^{2} sin (5 x)

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

求解步骤

\frac{d}{d x} (x^{2} sin (5 x))

使用微分乘法定则:

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

f = x^{2}, g = sin (5 x)

= \frac{d}{d x} (x^{2}) sin (5 x) + \frac{d}{d x} (sin (5 x)) x^{2}

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

\frac{d}{d x} (sin (5 x)) = cos (5 x) \cdot 5

= 2 x sin (5 x) + cos (5 x) \cdot 5 x^{2}

\frac{d y}{d x} = \frac{( x - 4 )}{y + 5}

\frac{t}{2 t + 3}

\int cos^{3} (4 θ) sin (4 θ) d θ

\frac{d y}{d x} = - x e^{- x + y}

y^{^{'}} = y (2 + y) t