derivative of (3x+5^3-5x)

解答

\frac{d}{d x} ((3 x + 5)^{3} - 5 x)

81 x^{2} + 270 x + 220

求解步骤

\frac{d}{d x} ((3 x + 5)^{3} - 5 x)

化简

(3 x + 5)^{3} - 5 x : 27 x^{3} + 135 x^{2} + 220 x + 125

= \frac{d}{d x} (27 x^{3} + 135 x^{2} + 220 x + 125)

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (27 x^{3}) + \frac{d}{d x} (135 x^{2}) + \frac{d}{d x} (220 x) + \frac{d}{d x} (125)

\frac{d}{d x} (27 x^{3}) = 81 x^{2}

\frac{d}{d x} (135 x^{2}) = 270 x

\frac{d}{d x} (220 x) = 220

\frac{d}{d x} (125) = 0

= 81 x^{2} + 270 x + 220 + 0

化简

= 81 x^{2} + 270 x + 220

\frac{\partial}{\partial x} (x e^{(\frac{y}{x})})

\int \frac{1}{cos ^{2} ( b ) x} d x

x \to 2 lim (- 5)

\int - cos (2 t) d t

\int \frac{1}{( 1 - x ) ( 2 - x )} d x