derivative of x^2+4x+12y-8

解答

\frac{d}{d x} (x^{2} + 4 x + 12 y - 8)

2 x + 12 \frac{d y}{d x} + 4

求解步骤

\frac{d}{d x} (x^{2} + 4 x + 12 y - 8)

使用微分加减法定则:

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

= \frac{d}{d x} (x^{2}) + \frac{d}{d x} (4 x) + \frac{d}{d x} (12 y) - \frac{d}{d x} (8)

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

\frac{d}{d x} (4 x) = 4

\frac{d}{d x} (12 y) = 12 \frac{d y}{d x}

\frac{d}{d x} (8) = 0

= 2 x + 4 + 12 \frac{d y}{d x} - 0

化简

= 2 x + 12 \frac{d y}{d x} + 4

\frac{\partial}{\partial x} (x^{2} y^{2} + 4 x^{2} - 3 x y)

f^{^{''}} (x) = a cos (2 x) + b sin (2 x)

n = 1 \sum \infty 3 (\frac{1}{4})^{n - 1}

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

d er i v a t i v e f (- x) = \frac{x}{x ^{2} + 1}