(\partial)/(\partial x)(2x^2*4x^3)

解答

\frac{\partial}{\partial x} (2 x^{2} \cdot 4 x^{3})

40 x^{4}

求解步骤

\frac{\partial}{\partial x} (2 x^{2} \cdot 4 x^{3})

化简

2 x^{2} \cdot 4 x^{3} : 8 x^{5}

= \frac{\partial}{\partial x} (8 x^{5})

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= 8 \frac{\partial}{\partial x} (x^{5})

使用幂法则:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 8 \cdot 5 x^{5 - 1}

化简

= 40 x^{4}

\int_{- 1}^{1} x^{2} + 1 d x

(sin (t)) y^{^{'}} + (cos (t)) y = 3 t (sin (t))

d er i v a t i v e f (x) = \frac{4 x + 2}{4 x - 2}

d er i v a t i v e arctan (t)

x \to - 1 lim ((x + 2)^{2})